Could someone please help me solve this?

Question

The one-to-one functions g and h are defined as follows.

g= (-9,-8), (-7, -6), (3, 5), (5, 9)

h(x) = 2x+9

Find the following.

g^-1(5)

h^-1(x)

(h^-1 o h) (-7)

Answer 1

g= (3,5) among other points

g^-1(5) = (5,3)

the inverse function switches x and y coordinates. If (x,y) is in g, then (y,x) in in g^-1

h=2x+9 switch h and x and solve for the new h

x=2h+9

2h = x-9

h = x/2 - 4.5

h^-1 = x/2 - 4.5

h^-1(h(-7) = -7

the inverse takes you back to where you started

much like x-7 -x = -7 addition and subtraction are inverses

h^-1 and h are inverses. You start with -7 and end with -7

h(x)= 2x+9

h^-1(x) = x/2-4.5

h(-7) = 2(-7)+9 = -14+9 = -5

h^-1(-5) = (-5)/2 -4.5 = -2.5-4.5 = -7