H(x)=f(g(x))? how do i do this?

Question

1. h(x)=(x+1)^2

2. h(x)=√(x+1)

3. h(x)=(1)/(x^2)

Answer 1

Ask 'what are the two operations I perform to evaluate the expression?'

For (x + 1)^2, you first evaluate g(x) = x + 1.

Then you evaluate f(x + 1) = (x + 1)^2.

Therefore f(x) = x^2.

1.

g(x) = x + 1

f(x) = x^2.

2.

g(x) = x + 1

f(x) = sqrt(x).

3.

g(x) = x^2

f(x) = 1 / x.