I need help with this question:

Question

Express below function in terms of f(x) if f(x)= x^2
y= 3(-4x-2)^2 + 5

Answer 1

let f(x) = z = x^2
so x = sqrt z and z always positive

y = 3 (-4 sqrt z-2)^2 + 5

y = 3(16 z + 16 sqrt z +4) + 5

y = 48 z + 48 z^.5+ 17

y = 48 f(x) +48 f(x)^.5 + 17

Answer 2

It's kind of confusing. Can you show me without putting z.

Answer 3

believe me, it is much less confusing using another symbol for x^2 then replacing it at the end.

Answer 4

You have

y= 3(-4x-2)^2 + 5
= 3(16x^2+16x+4)+5
= 48x^2+48x+17

Now, f = x^2, so x = √f
That makes

y = 48f + 48√f + 17