Inverse Functions Practice - Hun Kim Tutorials

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$f(x)=3x-2$ . Find $f^{-1}(x)$
Solution
$\frac{x+2}{3}$
f(x)=(x-2)^2, x\geq 2
1. Find $f^{-1}(x)$
  Solution
  $\sqrt{2}+2$
2. Domain and range of $f(x)$
  Solution
  $x\geq2$ and $y\geq0$
3. Domain and range of $f^{-1}(x)$
  Solution
  $x\geq0$ and $y\geq2$
The point (2,3) is on f(x)
1. What point must be on $f^{-1}(x)$ ?
  Solution
  $(3,2)$
2. What point must be on $y=2f\left(\frac{x}{2}-1\right)$ ?
  Solution
  $(6,6)$
3. What point must be on $3-3f^{-1}(2x)$ ?
  Solution
  $\left(\frac{3}{2},-3\right)$
See $f(x)$ below:

Sketch $f^{-1}(x)$ on top of the graph above
Solution
In general, $f(x)$ reflects $f^{-1}(x)$ along which line?
Solution
$y=x$
Simplify $y=f\left(f^{-1}(x)\right)$
Solution
$5$
$g(x)=x^2$ and $f(x)=x^{1/2}$
$h(x)=g\left(f(x)\right)$ . True or False: Since $g(x)$ and $f(x)$ “undo” each other, $h(-4)=-4$
Solution
False, $g$ has an undefined input
$f(x)=3e^{x-2}$ . Find $f^{-1}(x)$
Solution
$\ln x-\ln3+2$
Challenge: $f(x)=x^2+6x+2$ . Find $f^{-1}(x)$
Solution
Completing the square on $y$ we get the relation:
$f^{-1}(x)=\pm\sqrt{x+7}-3$