Question

If b(g(x)) = 5x^2 - 13, find b(x). Given that g(x)= x^2 - 2.

Answer 1

I got so far as to realize:

\[5x ^{2}-13 = b(x ^{2}-2)\]

I just don't know how to isolate b(x)

Answer 2

@phi

Answer 3

this seems like a hard problem.
b(x) is a function
and the idea is if we replace x with a complicated "x" (i.e. x^2-2) we will get out
5x^2-13

because we have x^2 in the answer, I would start by guessing
b(x) = x

then
b(x^2-2) gives x^2 -2
and that does not match 5x^2-13

maybe if we multiply by 5 in our guess?
b(x) = 5x

what do we get for b(x^2-2) now ?

Answer 4

i'm still lost