To determine the inverse, 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=(x-1)^2+2 Result: The inverse is a function.
Practice makes perfect
We will begin by finding the inverse of y. First, we need to switch x and y and solve for y.
y=sqrt(x-2)+1 → x=sqrt(y-2)+1The resulting equation will be the inverse of the given function.
Now that we 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 this case, for each x in domain of the inverse there is only one value of y in the range. Therefore, the inverse is a function in its domain.
