Cards In This Deck

• $\text{Condition required for a function }f(x)\text{ to have an inverse }{f}^{-1}(x)\text{?}$
  $\text{The function }f(x)\text{ must be one-to-one.}$
• $\text{When finding the inverse }{f}^{-1}(x)\text{ graphically, which line do you reflect }f(x)\text{ in?}$
  $\text{The line }y=x\text{.}$
• $$\begin{gathered} \text{True or False?} \\ \text{The domain of the inverse function }{f}^{-1}(x)\text{ is the same as the domain of the original function }f(x)\text{.} \end{gathered}$$
  $$\begin{gathered} \text{❌ False} \\ \text{✅ The domain of }{f}^{-1}(x)\text{ is the Range of }f(x)\text{.} \end{gathered}$$
• $$\begin{gathered} \text{True or False?} \\ \text{The solution to }f(x)=f^{-1}(x)\text{ can often be found by solving }f(x)=x\text{.} \end{gathered}$$
  $$\begin{gathered} \text{✅ True} \\ \text{Since the graphs of }f\text{ and }{f}^{-1}\text{ intersect on the line of reflection }y=x\text{, solving }f(x)=x\text{ is usually much simpler.} \end{gathered}$$
• $\text{First step to find the inverse function }{f}^{-1}(x)\text{ algebraically?}$
  $\text{Let }y=f(x)\text{ and rearrange the equation to make }x\text{ the subject.}$
• $$\begin{gathered} \text{True or False?} \\ \text{The inverse function of }f(x)=e^{x+2}\text{ is }{f}^{-1}(x)=\ln x+2\text{.} \end{gathered}$$
  $$\begin{gathered} \text{❌ False} \\ \text{✅ Correct Answer: }{f}^{-1}(x)=\ln x-2 \end{gathered}$$