Question

How do you solve this function : g[f(x)] if f(x) = 4x + 1 and `g(x) = 2x^2 - 5`?

Answer 1

`g(f(x)) = 32x^2+16x-3`

Explanation:

If
`color(white)("XXX")color(blue)(f(x))=color(blue)(4x+1)`
and
`color(white)("XXX")g(color(red)(x)) = 2color(red)(x)^2-5`

Then
`color(white)("XXX")g(color(blue)(f(x)))= 2(color(blue)(f(x)))^2-5`

`color(white)("XXXXXXX")=2(color(blue)(4x+1))^2-5`

`color(white)("XXXXXXX")=2(color(blue)(16x^2+8x+1))-5`

`color(white)("XXXXXXX")=32x^2+16x-3`