The function f(x) = 9x+5/x-8 is one to one

find an equation for f^-1(x), the inverse function

Question

The function f(x) = 9x+5/x-8 is one to one

find an equation for f^-1(x), the inverse function

asnaseer · Answer

first write this as:$$y=\frac{9x+5}{x-8}$$then swap the x and y's to get:$$x=\frac{9y+5}{y-8}$$now just rearrange this to get it in the form: y = f(x)

asnaseer · Answer

that will be your inverse function.

anonymous · Answer

im having trouble simplifying x = 9y+5 
                                                      -----
                                                       y-8

how do i solate y?

anonymous · Answer

@dylanlamoreaux , multiply both sides by (y-8) then distribute the x into y-8 on the left side

campbell_st · Answer

$$x = \frac{9y + 5}{x -8}$$

multiply both sides by (y - 8)

$$x(y - 8) = 9y + 5$$

expand and simplify

xy - 8x = 9y + 5

y( x -9) = 8x + 5

$$y =\frac{8x + 5}{x - 9}$$

asnaseer · Answer

Actually what @campbell_st said earlier is true - I didn't read the question fully. This is NOT a one-to-one function as the original function f(x) = (9x+5)/(x-8) leads to f(8) = $\pm\infty$ as x approaches 8 from the left/right.