What is the inverse of f(x) = x2 + 5 and is it a function?
1 answer:
Answer:
Step-by-step explanation:
The inverse of an equation is only a function if the original function is one-to-one. Meaning it passes the horizontal line test. Our equation is a parabola. While this original is in fact a function, it is not one-to-one. So that means that the inverse will not be a function. Let's find the inverse first, then we will verify its non-function status.
To find the inverse, switch the x and the y and solve for the new y:
and
which means that
Because you are taking the square root of y, you need to allow for both the positive and the negative of the square root of x - 5. Graph these 2 equations in your calculator and you will see that if we do not first restrict the domain of the original equation, our inverse will not be a function.
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