To algebraically determine the inverse of y, switch x and y and solve for y.
Inverse: y=± sqrt(x-5) Result:No, The inverse is not a function.
Practice makes perfect
We will begin by finding the inverse of y. We need to switch x and y and solve for y.
y=- x^2+5 → x= y^2+5The resulting equation will be the inverse of the given function.
Now that we have found the inverse of y, we will determine whether the inverse is a function. We shall recall that function is a relation where each input is related to exactly one output. In our case, we can see that for each x, there are two values of y.
If x=a, then y=± sqrt(a-5).
Therefore, the inverse of the function is not a function.
