evaluate the composite function for the indicated values of x:

Question

i(x)= (x-2) • g(x) h(x)= 3x²-11-i(x) f(x)= (2g-h)(x)

(i+h°f)(x) for x= -1, 0, 3

Answer 1

Hi Mona,

g or h is not defined in the problem so I can only simplify down to those variables, but here is what I would gather -

Determine (i+h°f)(x) :

(i+h°f)(x) = i(x) + h°f (x)

i(x) = (x-2) * g(x)

h°f (x) = h(f(x)) = 3(f(x))²-11-i(x)

h°f (x) = 3((2g-h)x)²-11-i(x)

h°f (x) = 3((2g-h)x)²-11- g(x)(x-2)

(i+h°f)(x) = (x-2) * g(x) + 3((2g-h)x)²-11 - g(x) * (x-2)

= 3(2gx-hx)² - 11

Plug in for x = -1,0,3

For x = -1

3(2gx-hx)² -11

3(2g(-1) - h(-1))² - 11

3(-2g+h)² - 11

For x = 0

3(2gx-hx)² -11

3(2g*0-h*0)² - 11

0 - 11

-11

For x = 3

3(2gx-hx)² - 11

3(2g*3 - h*3)² - 11

3(6g - 3h)² - 11