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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,​

Respuesta :

Answer:

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)

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