Sample quiz on inverse of a function
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1. Let $f(x)$ be a function. Its inverse is usually denoted by $\cdots$?
   
   A: $f^{-1}(x)$
   B: $f(-x)$
   C: $f\Big(\frac{1}{x}\Big)$
   D: $\frac{1}{f(x)}$
   
2. Find the inverse of the function given as ordered pairs: $\{(1,2),(2,3),(3,4),(4,5),(5,6)\}$
   
   A: $\{(1,2),(2,3),(3,4),(4,5),(5,6)\}$
   B: $\{(2,1),(3,2),(4,3),(5,4),(6,5)\}$
   C: $\{(1,\frac{1}{2}),(2,\frac{1}{3}),(3,\frac{1}{4}),(4,\frac{1}{5}),(5,\frac{1}{6})\}$
   D: $\{(1,\frac{1}{2}),(\frac{1}{2},\frac{1}{3}),(\frac{1}{3},\frac{1}{4}),(\frac{1}{4},\frac{1}{5}),(\frac{1}{5},\frac{1}{6})\}$
3. Let $f(x)=x$. Find the inverse of the function $f(x)$.
   
   A: $f^{-1}(x)=\frac{1}{x}$
   B: $f^{-1}(x)=x^2$
   C: $f^{-1}(x)=2x$
   D: $f^{-1}(x)=x$
4. Find the inverse of the function $f(x)=ax+b$, assuming both $a$ and $b$ are non-zero.
   
   A: $f^{-1}(x)=\frac{x-b}{a}$
   B: $f^{-1}(x)=\frac{x+b}{a}$
   C: $f^{-1}(x)=\frac{b-x}{a}$
   D: $f^{-1}(x)=\frac{a}{x-b}$
5. Find the inverse of the parent quadratic function $f(x)=x^2$
   
   A: $f^{-1}(x)=\pm x$
   B: $f^{-1}(x)=\pm\sqrt{\frac{1}{x}}$
   C: $f^{-1}(x)=\pm\sqrt{x}$
   D: $f^{-1}(x)=\sqrt{x}$
6. Is the inverse of a function also a function?
   
   A: YES, all the time
   B: NO, not always
   C: NO, never possible
   D: YES, but only linear functions
7. Let $f(x)=x^2-1$. Find $f^{-1}(x)$.
   
   A: $f^{-1}(x)=\pm\sqrt{x}+1$
   B: $f^{-1}(x)=\pm\sqrt{x-1}$
   C: $f^{-1}(x)=\pm\sqrt{x+1}$
   D: $f^{-1}(x)=\pm\sqrt{x^2+1}$
8. Let $f(x)=x^2+2x+1$. Find $f^{-1}(x)$.
   
   A: $f^{-1}(x)=-1-\sqrt{x}$
   B: $f^{-1}(x)=-1\pm\sqrt{x}$
   C: $f^{-1}(x)=-1+\sqrt{x}$
   D: $f^{-1}(x)=-1\pm\sqrt{2x}$
9. Let $f(x)=x^2+6x+1$. Find $f^{-1}(x)$.
   
   A: $f^{-1}(x)=-3\pm\sqrt{x+8}$
   B: $f^{-1}(x)=-3\pm\sqrt{x-8}$
   C: $f^{-1}(x)=-3\pm\sqrt{8-x}$
   D: $f^{-1}(x)=-3\pm\sqrt{x+6}$
10. Let $f(x)=\frac{x+1}{2x-1}$. Find $f^{-1}(x)$.
    
    A: $f^{-1}(x)=\frac{x+1}{2x+1}$
    B: $f^{-1}(x)=\frac{2x-1}{x+1}$
    C: $f^{-1}(x)=\frac{x-1}{2x-1}$
    D: $f^{-1}(x)=\frac{x+1}{2x-1}$