Chapter 4 - Inverse, Exponential, and Logarithmic Functions - 4.1 Inverse Functions - 4.1 Exercises - Page 416: 20

not one-to-one

When we see $x^{2}$ in the function expression, our first thought should be "this is probably not one-to-one", because, for example, $1^{2}=(-1)^{2}$... $f(x)=-\sqrt{100-x^{2}}$ is defined for $x=1$ and $x=-1,$ (different values from the domain ...) $f(1)=-\sqrt{99}=f(-1)$ ( ... have the same function value)