The topic of inverse functions is all about 
interchanging x-coordinates and y-coordinates.

g={(-6,5),(1,-7),(5,-4),(8,-8)}

Find:

g-1(5)=

To find g-1, just swap the coordinates of each point:

g-1 = {(5,-6),(-7,1),(-4,5),(-8,8)}

So g-1(5) = -6

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h(x) = 2x+13

Write y for h(x)

y = 2x+13

Interchange x and y

x = 2y+13

Solve for y











h-1(x)=

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(h-1∘h)(-8)=

The composition of a function with its inverse or vice-versa
is the identity function y = x, sometimes written I(x) = x.

Therefore, the output is the same as the input.

(h-1∘h)(-8)= I(-8) = -8.

Edwin