Question Type 4: Finding the inverse with domain restriction Exercises

Find the inverse function $f^{-1}(x)$ for $f(x)=-2(x-3)^2+1$ with the domain restriction $x\ge 3$. State the domain of $f^{-1}$.

Find the inverse function $f^{-1}(x)$ for $f(x)=\ln(10-x^2)$ with the domain restriction $0<x<\sqrt{10}$. State the domain of $f^{-1}$.

Find the inverse function $f^{-1}(x)$ for $f(x)=\sin\left(2x-\frac{\pi}{6}\right)$ with the domain restriction $-\frac{\pi}{6}\le x\le \frac{\pi}{3}$. State the domain of $f^{-1}$.

Find the inverse function $f^{-1}(x)$ for $f(x)=\cos\left(2x+\frac{\pi}{4}\right)$ with the domain restriction $-\frac{\pi}{8}\le x\le \frac{3\pi}{8}$. State the domain of $f^{-1}$.

Find the inverse function $f^{-1}(x)$ for $f(x)=4\ln(x^2-9)$ with the domain restriction $x>3$. State the domain of $f^{-1}$.

Find the inverse function $f^{-1}(x)$ for $f(x)=\sqrt{(x-2)^2+4}$ with the domain restriction $x\ge 2$. State the domain of $f^{-1}$.

Find the inverse function $f^{-1}(x)$ for $f(x)=3\ln(2-x)+5$ with the domain restriction $x<2$. State the domain of $f^{-1}$.

Find the inverse function $f^{-1}(x)$ for $f(x)=|3x-2|+1$ with the domain restriction $x\ge \frac{2}{3}$. State the domain of $f^{-1}$.

Find the inverse function $f^{-1}(x)$ for $f(x)=x+\dfrac{1}{x}$ with the domain restriction $x\ge 1$. State the domain of $f^{-1}$.

Find the inverse function $f^{-1}(x)$ for $f(x)=\ln\left(\dfrac{x-1}{x+1}\right)$ with the domain restriction $x>1$. State the domain of $f^{-1}$.

Find the inverse function $f^{-1}(x)$ for $f(x)=(x-2)^2+5$ with the domain restriction $x\ge 2$. State the domain of $f^{-1}$.

Find the inverse function $f^{-1}(x)$ for $f(x)=e^{x^2-1}$ with the domain restriction $x\ge 0$. State the domain of $f^{-1}$.

Find the inverse function $f^{-1}(x)$ for $f(x)=-(x+1)^2+7$ with the domain restriction $x\le -1$. State the domain of $f^{-1}$.