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

Step-by-step explanation:

f(x) = 4-x

g(x) = h[tex]x^{2}[/tex]+k

g(f(x)) = 2[tex]x^{2}[/tex]-16x+26

so put f(x) in g(x)

h[tex](4-x)^{2}[/tex]+k

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

h([tex]x^{2}[/tex]-8x+16)+k

if h = 2 , then

2[tex]x^{2}[/tex]-16x+32 + k

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

2[tex]x^{2}[/tex]-16x+32 + (-6)

2[tex]x^{2}[/tex]-16x+32 - 6

2[tex]x^{2}[/tex]-16x+26

h=2

k=(-6)