To algebraically determine the inverse of a function, 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(5x) 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=x^2/5 → x=y^2/5
The resulting equation will be the inverse of the given function.
lc y ≥ 0:y = sqrt(5x) & (I) y < 0:y = - (sqrt(5x)) & (II)
ly=sqrt(5x) y=-sqrt(5x)
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(5a).
Therefore, the inverse of the function is not a function.
