# Thread: Function Properties Not Inherited By Inverses

1. ## Function Properties Not Inherited By Inverses

Suppose that f has an inverse function f^(-1).For Each Of the Following Properties Give an example to show that f can have the property while its inverse does not

[a] f has a graph with a horizontal asymptote
[b] f has a domain all real numbers
[c] f has a graph that is bounded above
[d] f has a removable discontinuity at x=5

2. Originally Posted by Rimas
Suppose that f has an inverse function f^(-1).For Each Of the Following Properties Give an example to show that f can have the property while its inverse does not

[a] f has a graph with a horizontal asymptote
$\displaystyle f(x) = e^x$

[b] f has a domain all real numbers
$\displaystyle f(x) = x^2$

[c] f has a graph that is bounded above
$\displaystyle f(x) = -x^2$

[c] f has a removable discontinuity at x = 5
$\displaystyle f(x) = \left \{ \begin{array}{lr} x - 5 & \mbox{ if } x \ne 5 \\ x & \mbox{ if } x = 5 \end{array}\right.$