Question

Let f(x) = x² + 3x - 2 and g(x) = √√x + 1. Find and simplify: (g°f)(x)

Answer 1

Answer:

(g ° f)(x)​ = √ x^2 + 3x - 1

Explanation:

The expression (g ° f)(x)​ is the same as g(f(x)).

Therefore, to evaluate (g ° f)(x)​, we replace x in g(x) with f(x).

Now,

$g(x)=\sqrt{x+1}.$$\therefore g(f(x))=\sqrt{f(x)+1}$

Since f(x) = x² + 3x - 2, the above gives

$g(f(x))=\sqrt{x^2+3x-2+1}$

which simplifies to give

$g(f(x))=\sqrt{x^2+3x-1}$

Hence,

$\boxed{(g\circ f)(x)=x^2+3x-1.}$

which is our answer!