Question

(q32) What is the inverse of the function

Answer 1

A. 5x/(1 -x)

Explanation:

You want the inverse of function f(x) = x/(x+5).

Inverse function

The inverse of the function will have a graph that is the reflection of the function's graph over the line y = x. The inverse function can be found by swapping y and x, then solving for y:

x = f(y) . . . . . . y is the inverse function

x = y/(y +5) . . . . . use the function definition

xy +5x = y . . . . multiply by (y+5)

y(x -1) +5x = 0 . . . . . . . subtract y and factor

y = -5x/(x -1) = 5x/(1 -x) . . . . . divide by the coefficient of y

The inverse function is ...

`f^(-1)(x)=(5x)/(1-x)`

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Additional comment

You will notice the function f(x) has a vertical asymptote at x = -5. That means the inverse function will have a horizontal asymptote at y = -5. The only answer choice for which that is true is A.

In the attached graph, the original function f(x) is red; the inverse function is blue. Notice the symmetry and the asymptotes.

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