Question

What is the multiplicative inverse of `5/(x-2)`?

Answer 1

Reverse function of `f(x)=5/x-2` is `g(x)=5/(x+2)`

Explanation:

We have `f(x)=5/x-2`

Hence `5/x=f(x)+2`

or `x=5/(f(x)+2)`

Hence reverse function of `f(x)=5/x-2` is

`g(x)=5/(x+2)`

Answer 2

`f(x)^-1 =1/(5/(x-2))=(x-2)/5`

Explanation:

The inverse of a real number for all non-zero real numbers is the number when multiplied to the original gives a product of 1.

In simpler terms, if asked to find the inverse of the number 3

then: `3x=1` where `x` is the inverse.

Solving for `x`, `(3x)/3=1/3`, `x=1/3`

Remember that `3=3/1` so if we multiply the number 3 by its inverse in this manner:

`(3/1)(1/3)=1`

We can tell by this that a simple rule of thumb for the inverse of a number is just the numerator and denominators are exchanged. This is because the numerator and denominators cancel each other out respectively `3/1*1/3=(3*1)/(3*1)=3/3=1`