Question

Match each function with the corresponding function formula when h(x) = 2 – 2x and g(x) = –2 x + 2.

Answer 1

The function formulas are h(x) = 2 - 2x and g(x) = -2x + 2.

Step-by-step explanation:

h(x) = 2 - 2x

g(x) = -2x + 2

Even function times an even function produces an even function, Odd function times an odd function produces an even function.

Answer 2

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