Suppose hx4x8x7 Evaluate h19 Enter the exact answer in fract

Suppose h(x)=4-x+8/x-7. Evaluate h^-1(9). Enter the exact answer in fraction form if necessary. h^-1(9)= Evaluate [h(9)]^-1. Enter the exact answer in fraction form if necessary.

Solution

given h(x) = 4 - (x+8)/(x-7)

let us say h(x) =y

then x = h^-1(x)

y= 4 - (x+8)/(x-7)

y-4 = -(x+8)/(x-7)

(y-4)(x-7) = -x -8

xy -7y-4x+28 =-x-8

y(x-7) = -x-8 +4x -28

y(x-7) = 3x-36

y = 3x-36/(x-7)

so this is h^-(y)

h^-1(x) = (3y -36) /(x-7)

now plug x=9

h^-1(9) = (3x9 -36)/(9-7)

= (27-36)/2

= -9/2

=-4.5

b). directly plug in h(x)

h(9) = 4- (9+8)/(9-7)

h(9) = 4 - 15/2

h(9) = -7/2

h(9) =-3.5

[h(9)]^-1 = -1/3.5