Part II: The Answers
134
Answers
1–100
22.
y = x
2
– 4, x ≥ 0
When determining whether a function has an inverse, consider the domain of the given
function. Some functions don’t pass the horizontal line test — and therefore don’t have
an inverse — unless the domain is restricted. The function y = x
2
– 4 doesn’t pass the
horizontal line test; however, if you restrict the domain to x ≥ 0, then y = x
2
– 4 does
pass the horizontal line test (and therefore has an inverse), because you’re getting
only the right half of the parabola.
23.
y = tan
−1 
x
Of the given functions, only the function y = tan
−1 
x passes the horizontal line test.
Therefore, this function is one-to-one and has an inverse.