If f(x) = (x - 1)2 and g(x) = √x

Question

then (g o f)(x) =? 

Answer 1

The functions are f (x ) = (x - 1)²  and g (x ) =√x

 ( g of )(x ) = g (f (x ))

Substitute the expression for functioning f  (in this case (x - 1)²) for f (x ) in the composition.

= g ((x - 1)²)

Substitute the expression for functioning g  (in this case √x) for g (x ) in the composition.

= √(x - 1)²

= x - 1

( g of )(x ) = x - 1.