Question

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

Answer 1

(g ° f)(x)​ = √ x^2 + 3x - 1

Step-by-step 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)=√(x+1).`
`\therefore g(f(x))=√(f(x)+1)`

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

`g(f(x))=√(x^2+3x-2+1)`

which simplifies to give

`g(f(x))=√(x^2+3x-1)`

Hence,

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

which is our answer!