Question

If f(x) = 2x – 1 and g(x) = x^2 – 2, find [g ◦ f](x).

Answer 1

`(g\circ f)(x)=(2x-1)^2-2=4x^2-4x+1-2=4x^2-4x-1`

Answer 2

`4x^2 -4x -1`

Explanation:

Given functions,

`f(x) = 2x - 1-----(1)`

`g(x) = x^2 -2-----(2)`

∵ (gof)(x) = g[f(x)] ( Composition of functions )

`\implies (gof)(x) = g(2x-1)` ( From equation (1) )

`=(2x-1)^2 - 2` ( From equation (2) )

`=4x^2 + 1 - 4x - 2`

`=4x^2 -4x -1`