Precalculus questions with steps and explanations please

Question

1. Determine the domain and range for the inverse of f(x)=(1/3x)-1
2. The function f(x)=(x+8)^2-1 is not one to one. Identify a restricted domain that makes the function one to one and find the inverse function.
3. find (g o f)(x) when f(x)=sqrt(x+1) and g(x)=(x^2+3)/x
4. Find (f o g)(x) and its domain when f(x)=x^2+4 and g(x)=sqrt(x+2)

Answer 1

For 1) the domain of the inverse function will be the range of the original function and the range of the inverse function will be the domain of the original function. So find the domain and range of the original function and swap them.

For 2), the easiest way is to graph the function (use desmos) and look to see where the horizontal line test results in a problem. Then restrict the domain to prevent it from being a problem.

For 3), starting with g(x), plug if f(x) wherever you see an "x" in g(x). Then simplify.

For 4), starting with f(x), plug if g(x) wherever you see an "x" in f(x). Then simplify.