Let f ( x ) = x + 5 / x + 8 , f^-1(-6)=

Answer 1

Here, we want to start off by finding f^-1. We can write f(x)=(x+5)/(x+8) and use y=(x+5)/(x+8) to find the inverse. We do that by putting x wherever there is a y and y wherever there is an x. So we would get:

x=(y+5)/(y+8).

Now we solve for y.

Multiply by (y+8) on both sides to get:

x(y+8)=y+5

Distribute and move the y-terms to one side and everything else to the other side:

xy-y=5-8x

Factor out the y to get y(x-1) on the left hand side of the equal sign. Then divide by (x-1) on both sides to get y by itself:

* y=(5-8x)/(x-1) *

Finally, we plug in x=-6 into the * * equation right above to get f^-1(-6)

f^-1(6)=(5-8(-6))/((-6)-1)

= (5+48)/(-7)

= -53/7