Suppose f(g(x) = 2x² -16x + 17 and g(x) = x - 4. Find f(x)?

Question

I just want to know how you can get f(x) when f(g(x) and g(x) is given

Answer 1

f (x - 4) = 2x² - 16x + 17

Let y = x - 4

f (y) = 2 (y + 4)² - 16 (y + 4) + 17

f (y) = 2 (y² + 8y + 16) - 16 y - 64 + 17

f (y) = 2 y² - 15

f (x) = 2 x² - 15

Answer 2

See if you can rearrange f(g(x)) so that g(x) appears in it somewhere.

f(g(x)) = 2x^2 - 16x + 17

f(g(x)) = 2(x^2 - 8x) + 17

f(g(x)) = 2(x^2 - 8x + 16) + 17 - 32

f(g(x)) = 2(x-4)^2 - 15

So it looks like f(x) = 2x^2 - 15

Answer 3

f(g(x)) = 2x^2 - 34x + 17

f(g(x)) = 2(x^2 - 8x) + 17

f(g(x)) = 2(x^2 - 8x + 16) + 17 - 33

f(g(x)) = 2(x-4)^2 - 15

f(x) = 4x^2 - 13