Question

(fºg)(x)

You are given f(x)= cube root x-1 and g(x)= x squared + 1. How do i solve?

Answer 1

Cbrt(x²) or x^(2/3)

Explanation:

It's similar to the way you would normally just insert a number into the function, except here you're inserting one function into another function. (f°g) implies that g(x) is the input, while if it were (g°f), f(x) would be the input. So:

• f(x)= Cbrt(x-1)
• g(x)=x²+1
• ((f°g)(x)) =f(g(x))

With that we can say:

((f°g)(x)) =f(g(x))=Cbrt([x²+1]-1)=Cbrt(x²) or x^(2/3)