Question

Given f(x) = 1/x and g(x) = sqrt(x), find the domain for

Answer 1

Basically, the restrictions on the domain of each function is a restriction on the domain of the composition of \(\left(f \circ g\right) (x)\)

Answer 2

In other words, \(x \nleq 0\) is the combined restriction for both f and g. Now once we compose the function, we might find yet another restriction. Can you compose the function so that we can find the remaining restriction?

Answer 3

it would be 1/sqrt(x)?

Answer 4

Yes, good. And basically, we've covered the combined restriction for the function. So that means the domain of the function is x > 0

Answer 5

I'm referring to the domain of \(h(x) = \left(f \circ g\right) (x)\)

Answer 6

The new function we produced after composition.

Answer 7

so would it be . I have to put it in that form of an answer