To algebraically determine the inverse, of switch x and y and solve for y. A function is a relation where each input is related to exactly one output.
Inverse of the Function: y=±sqrt(x2) Result: The inverse is not a function.
Practice makes perfect
We will begin by finding the inverse of y. First, we will switch x and y and solve for y.
y=2( x)^2 → x=2( y)^2
The resulting equation will be the inverse of the given function.
Now that we have found the inverse of y, we will determine if it is also a function.
Is the Inverse a Function?
A function is a relation where each input is related to exactly one output. In our case, we can see that for each x in the inverse, there are two values of y.
If x=a, then y=± sqrt(a2).
Therefore, the inverse of the function is not a function.
