Question 1165631
<pre>
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<sup>-1</sup>(5)=

To find g<sup>-1</sup>, just swap the coordinates of each point:

g<sup>-1</sup> = {(5,-6),(-7,1),(-4,5),(-8,8)}

So g<sup>-1</sup>(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

{{{x=2y+13}}}

{{{2y+13=x}}}

{{{2y=x-13}}}

{{{(2y)/2 = (x-13)/2}}}

{{{y=(x-13)/2}}}

h<sup>-1</sup>(x)={{{(x-13)/2}}}

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(h<sup>-1</sup>∘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<sup>-1</sup>∘h)(-8)= I(-8) = -8.

Edwin</pre>