Question

If f(x)= x^2 -1 and g (x) =2x +1, show that f[g(x)]=4x(x+1).

Answer 1

Given:

$f(x)=x^2-1,\quad g(x)=2x+1$

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