Inverse functions  Relations and Functions
Inverse functions
An inverse function is a function that reverses all the operations of another function. Therefore, an inverse function has all the points of another function, except that the x and y values are reversed.
Lessons

a)
Sketch the graph of the inverse $y = {f^{  1}}\left( x \right)$ in 2 ways:
i) by reflecting $f\left( x \right)$ in the line $y = x$
ii) by switching the x and y coordinates for each point on $f\left( x \right)$ 
b)
Is $f\left( x \right)$ a function?
Is ${f^{  1}}\left( x \right)$ a function?


3.
Consider the quadratic function: $f(x) = (x+4)^2 + 2$

4.
Determine the equation of the inverse.
Algebraically determine the equation of the inverse ${f^{  1}}\left( x \right)$, given: