Question

The functions f and g are defined by f: x = 4 - x and g: x = hx² + k. If the composite function gf is given by gf: x + 2x² - 16x + 26, find

(a) the value of h and of k,​

Answer 1

Explanation:

f(x) = 4-x

g(x) = h
`x^(2)`+k

g(f(x)) = 2
`x^(2)`-16x+26

so put f(x) in g(x)

h
`(4-x)^(2)`+k

h((4-x)(4-x) + k

h(
`x^(2)`-8x+16)+k

if h = 2 , then

2
`x^(2)`-16x+32 + k

and we want 26 instead of 32 so subtract 6 so K = (-6)

2
`x^(2)`-16x+32 + (-6)

2
`x^(2)`-16x+32 - 6

2
`x^(2)`-16x+26

h=2

k=(-6)