All High School Math Resources
Example Question #1 : Understanding Inverse Functions
Let . What is ?
We are asked to find , which is the inverse of a function.
In order to find the inverse, the first thing we want to do is replace f(x) with y. (This usually makes it easier to separate x from its function.).
Next, we will swap x and y.
Then, we will solve for y. The expression that we determine will be equal to .
Subtract 5 from both sides.
Multiply both sides by -1.
We need to raise both sides of the equation to the 1/3 power in order to remove the exponent on the right side.
We will apply the general property of exponents which states that .
Laslty, we will subtract one from both sides.
The expression equal to y is equal to the inverse of the original function f(x). Thus, we can replace y with .
The answer is .
Example Question #2 : Understanding Inverse Functions
What is the inverse of ?
The inverse of requires us to interchange and and then solve for .
Then solve for :
Example Question #3 : Understanding Inverse Functions
If , what is ?
To find the inverse of a function, exchange the and variables and then solve for .