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: $f^{-1}(x)=\frac{x+1}{2x-1}$