IB Mathematics Applications & Interpretation Question Type 4: Finding the Inverse Functions Including Their Domains and Range Exercises

Find the inverse of $f(x)={\log }_2(5x-1)$, and state the domain and range of $f$ and $f^{-1}$.

Find the inverse function of $f(x)=(x-2{)}^3+1$. Determine the domain and range of $f$ and $f^{-1}$.

Find the inverse of $f(x)=e^x+4$, and determine the domain and range of $f$ and $f^{-1}$.

Find the inverse of $f(x)=\sqrt{3x-1}$, and state the domain and range of $f$ and its inverse.

Find the inverse of $f(x)=4e^x+32$ for $0<x<1$, and state the domain and range of $f$ and $f^{-1}$.

Find the inverse of $f(x)=\ln (2x+3)$, and give domain and range for both functions.

Given $f(x)=x^2+1$ with $x\ge 0$, find $f^{-1}(x)$ and state domains and ranges.

Find the inverse of $f(x)=\sqrt{2x-3}$ for $x\ge \frac{3}{2}$, and give all domain and range restrictions.

Find the inverse of $f(x)=\frac{x+1}{x-2}$, stating domain and range of $f$ and $f^{-1}$.

Find the inverse of $f(x)=\frac{3x+5}{2}$ and give domains and ranges.

Find the inverse function of $f(x)=\frac{1}{x+2}$, stating all domain and range restrictions for $f$ and $f^{-1}$.

Find the inverse function of $f(x)=5x-7$. Determine the domain and range of $f$ and $f^{-1}$.