Match each function with the corresponding function formula when h(x)=5-3x and g(x)=-3+5

k(x) = (3g + 5h)(x) ⇒ (1)

k(x) = (5h - 3g)(x) ⇒ (3)

k(x) = (h - g)(x) ⇒ (2)

k(x) = (g + h)(x) ⇒ (4)

k(x) = (5g + 3h)(x) ⇒ (5)

k(x) = (3h - 5g)(x) ⇒ (6)

Step-by-step explanation:

* To solve this problem we will substitute h(x) and g(x) in k(x) in the

  right column to find the corresponding function formula in the

  left column

∵ h(x) = 5 - 3x

∵ g(x) = -3^x + 5

- Lets start with the right column

# k(x) = (3g + 5h)(x)

∵ g(x) = -3^x + 5

∵ 3g(x) = 3[-3^x + 5] = [3 × -3^x + 3 × 5]

- Lets simplify 3 × -3^x

 take the negative out -(3 × 3^x), and use the rule a^n × a^m = a^(n+m)

∴ -3(3 × 3^x) = -(3^x+1)

∴ 3g(x) = -3^x+1 + 15

∵ h(x) = 5 - 3x

∵ 5h(x) = 5[5 - 3x] = [5 × 5 - 5 × 3x] = 25 - 15x

- Now substitute 3g(x) and 5h(x) in k(x)

∵ k(x) = (3g + 5h)(x)

∴ k(x) = -3^x+1 + 15 + 25 - 15x ⇒ simplify

∴ k(x) = 40 - 3^x+1 - 15x

∴ k(x) = 40 - 3^x+1 - 15x ⇒ k(x) = (3g + 5h)(x)

* k(x) = (3g + 5h)(x) ⇒ (1)

# k(x) = (5h - 3g)(x)

∵ 5h(x) = 25 - 15x

∵ 3g(x) = -3^x+1 + 15

∵ k(x) = (5h - 3g)(x)

∴ k(x) = 25 - 15x - (-3^x+1 + 15) = 25 -15x + 3^x+1 - 15 ⇒ simplify

∴ k(x) = 10 + 3^x+1 - 15x

∴ k(x) = 10 + 3^x+1 - 15x ⇒ k(x) = (5h - 3g)(x)

* k(x) = (5h - 3g)(x) ⇒ (3)

# k(x) = (h - g)(x)

∵ h(x) = 5 - 3x

∵ g(x) = -3^x + 5

∵ k(x) = (h - g)(x)

∴ k(x) = 5 - 3x - (-3^x + 5) = 5 - 3x + 3^x - 5 ⇒ simplify

∴ k(x) = 3^x - 3x

∴ k(x)= 3^x - 3x ⇒ k(x) = (h - g)(x)

* k(x) = (h - g)(x) ⇒ (2)

# k(x) = (g + h)(x)

∵ h(x) = 5 - 3x

∵ g(x) = -3^x + 5

∵ k(x) = (g + h)(x)

∴ k(x) = -3^x + 5 + 5 - 3x ⇒ simplify

∴ k(x) = 10 - 3^x - 3x

∴ k(x)= 10 - 3^x - 3x ⇒ k(x) = (g + h)(x)

* k(x) = (g + h)(x) ⇒ (4)

# k(x) = (5g + 3h)(x)

∵ g(x) = -3^x + 5

∵ 5g(x) = 5[-3^x + 5] = [5 × -3^x + 5 × 5] = 5(-3^x) + 25

∴ 5g(x) = -5(3^x) + 25

∵ h(x) = 5 - 3x

∵ 3h(x) = 3[5 - 3x] = [3 × 5 - 3 × 3x] = 15 - 9x

- Now substitute 5g(x) and 3h(x) in k(x)

∵ k(x) = (5g + 3h)(x)

∴ k(x) = -5(3^x) + 25 + 15 - 9x ⇒ simplify

∴ k(x) = 40 - 5(3^x) - 9x

∴ k(x) = 40 - 5(3^x) - 9x ⇒ k(x) = (5g + 3h)(x)

* k(x) = (5g + 3h)(x) ⇒ (5)

# k(x) = (3h - 5g)(x)

∵ 3h(x) = 15 - 9x

∵ 5g(x) = -5(3^x) + 25

∵ k(x) = (3h - 5g)(x)

∴ k(x) = 15 - 9x - [-5(3^x) + 25] = 15 - 9x + 5(3^x) - 25 ⇒ simplify

∴ k(x) = 5(3^x) - 9x - 10

∴ k(x) = 5(3^x) - 9x - 10 ⇒ k(x) = (3h - 5g)(x)

* k(x) = (3h - 5g)(x) ⇒ (6)

I hope this helps

Step-by-step explanation:

1) g=h−k

2)g=−h+k

3) g=h−k/2

4)g=−h+k/2

5) g=2h−k/2

6)g=h+k

1 - 3, 2 - 5, 3 - 4, 4 - 6, 5 - 1, 6 - 2.

Step-by-step explanation:

We have,

h(x) = 5-3x and

So, according to the options, we have,

1. k(x) = (5g + 3h)(x)

Now,

i.e.

i.e.

i.e.

2. k(x) = (3h - 5g)(x)

Now,

i.e.

i.e.

i.e.

3. k(x) = (3g + 5h)(x)

Now,

i.e.

i.e.

i.e.

4. k(x) = (5h - 3g)(x)

Now,

i.e.

i.e.

i.e.

5. k(x) = (h - g)(x)

Now,

i.e.

i.e.

i.e.

6. k(x) = (g + h)(x)

Now,

i.e.

i.e.

Thus, we have the matches as,

1. k(x) = (5g + 3h)(x)  ----------------  5. k(x)=40-5(3^x)-9x

2. k(x) = (3h - 5g)(x)  ----------------  6. k(x)=5(3^x)-9x-10

3. k(x) = (3g + 5h)(x) ----------------   1. k(x)=40-3^x+1-15x

4. k(x) = (5h - 3g)(x)  -----------------  3. k(x)=10+3^x+1-15x

5. k(x) = (h - g)(x)   -----------------  2. k(x)=3^x-3x

6. k(x) = (g + h)(x)   ----------------- 4. k(x)=10-3^x-3x

1 -> f

2 -> a

3 -> d

4 -> b

5 -> e

6 -> c

Step-by-step explanation:

We are given:

h(x) = 2 - 2x and g(x) = -2^x+2

a) k(x)= (g-h)(x) = g(x) - h(x)

              = -2^x+2 - (2 - 2x)

              = -2^x+2 - 2 + 2x

              = -2^x+2x or 2x-2^x

k(x) = 2x-2^x = (g-h)(x)

So, 2 matches with a

b) k(x)= (g+h)(x) = g(x) + h(x)

              = -2^x+2 + (2 - 2x)

              = -2^x+2 + 2 - 2x

              = -2^x+4-2x or 4 - 2^x -2x

So, k(x) = 4 - 2^x -2x = (g+h)(x)

So, 4 matches with b

c) k(x)= (2h - 2g)(x) = 2h(x) - 2g(x)

              =  2(2 - 2x)-2(-2^x+2)

              = 4 - 4x+2.2^x-4

              = -4x+2^x+1 or 2^x+1-4x

So, k(x) = 2^x+1-4x = (2h - 2g)(x)

So, 6 matches with c

d) k(x) = (h-2g)(x) = h(x) - 2g(x)

         = (2 - 2x)-2(-2^x+2)

         = 2 - 2x+2.2^x-4

         = -2-2x+2^x+1

         = 2^x+1-2x-2

So, k(x) = 2^x+1-2x-2 = (h-2g)(x)

So, 3 matches with d

e) k(x) = (h-g)(x) = h(x) - g(x)

          = (2 - 2x)-(-2^x+2)

              = 2 - 2x+2^x-2

              = -2x+2^x or 2^x-2x

So, k(x) =  2^x-2x = (h-g)(x)

So, 5 matches with e

f) k(x) = (2g+h)(x) = 2g(x)+h(x)

          = 2(-2^x+2) + (2 - 2x)

          = -2.2^x+4 + 2 - 2x

          = -2^x+1+6-2x or 6 - 2^x+1-2x

So, k(x) = 6 - 2^x+1-2x = (2g+h)(x)

So, 1 matches with f

1) 6 - 2^(x + 1) - 2x = (2g - h)(x)

2) 2x - 2^x = (g - h)(x)

3) 2^(x + 1) - 2x - 2 = (h - 2g)(x)

4) 4 - 2^x - 2x = (g + h)(x)

5) 2^x - 2x = (h - g)(x)

6) 2^(x + 1) - 4x = (2h - 2g)(x)

Step-by-step explanation:

* Lets use right column to find the corresponding function in the

 left column

∵ h(x) = 2 - 2x

∵ g(x) = -2^x + 2

# k(x) = (g - h)(x)

∵ k(x) = g(x) - h(x)

∴ k(x) = -2^x + 2 - (2 - 2x) ⇒ multiply the -ve sign by the bracket

- Remember -ve × +ve = -ve and -ve × -ve = +ve

∴ k(x) = -2^x + 2 - 2 + 2x

∴ k(x) = -2^x + 2x ⇒ (2)

∴ k(x) = (g - h)(x) ⇒ (2)

* 2x - 2^x = (g - h)(x)

# k(x) = (g + h)(x)

∵ k(x) = g(x) + h(x)

∴ k(x) = -2^x + 2 + (2 - 2x) ⇒ simplify

∴ k(x) = -2^x + 2 + 2 - 2x

∴ k(x) = -2^x + 4 - 2x ⇒ (4)

∴ k(x) = (g + h)(x) ⇒ (4)

* 4 - 2^x - 2x = (g + h)(x)

# k(x) = (2h - 2g)(x)

∵ k(x) = 2h(x) - 2g(x)

- Lets find 2h(x) and 2g(x)

∵ 2h(x) = 2[2 - 2x] = 2(2) - 2(2x) = 4 - 4x

∵ 2g(x) = 2[-2^x + 2] = 2(-2^x) + 2(2)

- Remember a^n × a^m = a^(n + m)

∴ 2g(x) = 2(-2^x) + 4 = - (2 × 2^x) + 4 = - 2^(x + 1) + 4

∴ k(x) = 4 - 4x - [-2^(x + 1) + 4] ⇒ simplify

∴ k(x) = 4 - 4x + 2^(x + 1) - 4

∴ k(x) = 2^(x + 1) - 4x ⇒ (6)

∴ k(x) = (2h - 2g)(x) ⇒ (6)

* 2^(x + 1) - 4x = (2h - 2g)(x)

# k(x) = (h - 2g)(x)

∵ k(x) = h(x) - 2g(x)

∵ h(x) = 2 - 2x =

∴ 2g(x) = - 2^(x + 1) + 4

∴ k(x) = 2 - 2x - [-2^(x + 1) + 4] ⇒ simplify

∴ k(x) = 2 - 2x + 2^(x + 1) - 4

∴ k(x) = 2^(x + 1) - 2x - 2 ⇒ (3)

∴ k(x) = (h - 2g)(x) ⇒ (3)

* 2^(x + 1) - 2x - 2 = (h - 2g)(x)

# k(x) = (h - g)(x)

∵ k(x) = h(x) - g(x)

∴ k(x) = 2 - 2x - [-2^x + 2] ⇒ multiply the -ve sign by the bracket

- Remember -ve × +ve = -ve and -ve × -ve = +ve

∴ k(x) = 2 - 2x + 2^x - 2

∴ k(x) = 2^x - 2x ⇒ (5)

∴ k(x) = (h - g)(x) ⇒ (5)

* 2^x - 2x = (h - g)(x)

# k(x) = (2g + h)(x)

∵ k(x) = 2g(x) + h(x)

∵ h(x) = 2 - 2x =

∴ 2g(x) = - 2^(x + 1) + 4

∴ k(x) = -2^(x + 1) + 4 + 2 - 2x ⇒ simplify

∴ k(x) = -2^(x + 1) - 2x + 6

∴ k(x) = 6 - 2^(x + 1) - 2x ⇒ (1)

∴ k(x) = (2g + h)(x) ⇒ (1)

* 6 - 2^(x + 1) - 2x = (2g - h)(x)

1.k(x) = (3g + 5h)(x) = -24x+40

2.k(x) = (h - g)(x)  = 0

3.k(x) = (g + h)(x) = -6x+10

4.k(x) = (5g + 3h)(x) = -24x+40

5.k(x) = (3h - 5g)(x) = 6x-10

6.k(x) = (5h - 3g)(x) = 10-6x

Step-by-step explanation:

Given

h(x) = 5 - 3x

and

g(x) = -3 x + 5

1. k(x) = (3g + 5h)(x)

3*g(x) = 3(-3 x + 5)

=> -9x+15

5*h(x) = 5(5 - 3x)

=>25-15x

(3g + 5h)(x)=3*g(x)+5*h(x)

= -9x+15+25-15x

=-9x-15x+15+25

=-24x+40

2. k(x) = (h - g)(x)

(h - g)(x) = h(x) - g(x)

= 5 - 3x -(-3 x + 5)

=5-3x+3x-5

= 0

3. k(x) = (g + h)(x)

(g+h)x = g(x) + h(x)

= -3 x + 5 + 5 - 3x

= -6x+10

4. k(x) = (5g + 3h)(x)

5*g(x) = 5(-3 x + 5)

=-15x+25

3*h(x) = 3(5 - 3x)

=15-9x

(5g + 3h)(x) = 5*g(x) + 3*h(x)

= -15x+25+15-9x

= -15x-9x+25+15

=-24x+40

5. k(x) = (3h - 5g)(x)

(3h - 5g)(x) = 3*h(x)-5*g(x)

=15-9x-(-15x+25)

=15-9x+15x-25

=-9x+15x+15-25

=6x-10

6. k(x) = (5h - 3g)(x)

5*h(x)-3*g(x) = 25-15x - (-9x+15)

= 25-15x+9x-15

= 25-15-15x+9x

=10-6x

funtions: a, b, c...

formulas: 1, 2, 3...

A and 5, F and 2, B and 4, D and 1, C and 3, E and 6

k(x) = (h – g)(x)        k(x) = 2x - 2^x  

k(x) = (g + h)(x)  k(x) = 4 - 2^x - 2x

k(x) = (h – 2g)(x)  k(x) = 2^x+1 - 2x - 2

k(x) = (2g + h)(x)  k(x) = 6 - 2 ^x+1 - 2x

k(x) = (2h – 2g)(x)  k(x) = 2^x+1 - 4x

k(x) = (g – h)(x)        k(x) = 2x - 2^x

the correct functions are

h(x) = 3x + 2

g(x) = 2^x

proceed to calculate the different values ​​of K (x)

case 1) k(x) = g(x) ∘ h(x)

g(x) ∘ h(x)=g(h(x))

k(x) = [2]^[3x + 2]> is the option 4.k(x) = 2^(3x + 2 )

case 2) k(x) = g(x) + h(x)

k(x) = [2^x]+[3x + 2]=2^x+3x+2> is the option 1.) k(x) = 2^x + 3x + 4

case 3)k(x) = g(x) - h(x)

k(x) = [2^x]-[3x + 2]=2^x-3x-2> is the option 2.) k(x) = 2^x - 3x - 2

To match each functions with the corresponding function formula when h(x) = 5 - 3x and g(x) = -3 x + 5.

1. k(x) = (3h - 5g)(x)

  = = 3(5 - 3x)-5(-3 x + 5)

 = = 15 - 9x + 15x - 25

  K(x) = -10 + 6x

2.  k(x) = (h - g)(x)

    = = (5 - 3x) - (-3 x + 5)

 = = 0

k(x) = 0

3. k(x) = (5g + 3h)(x)

 = = 5(-3 x + 5)+3(5 - 3x)

 = = -15x + 25 + 15 - 9x

 k(x) = - 24x +40

4. k(x) = (3g + 5h)(x)

  =  = 3 (-3 x + 5) + 5(5 - 3x)

 = = -9x + 15 +25 -15x

 k(x) = -24x + 40

5.  k(x) = (g + h)(x)

   = = (-3 x + 5) + (5 - 3x)

k(x)  = -6x + 10

6.  k(x) = (5h - 3g)(x)

 = = 5(5 - 3x) - 3(-3 x + 5)

= =25 - 15x + 9x - 15

k(x) = 10 - 6x