# What is the inverse function of #f(x)=(x+1)^2#?

The function is not one-to-one. It does not have an inverse function. However,

By signing up, you agree to our Terms of Service and Privacy Policy

The function is not one-one and therefore there is not a unique inverse function.

First note that the slope (first derivative) is

Also note that

requires

that is

That is, the function is not a strictly rising or a strictly descending one.

That is, it is not bijective (one-one).

That is, there is no single inverse function if the domain is taken as the reals.

This implies

which in turn implies

or

By signing up, you agree to our Terms of Service and Privacy Policy

The inverse function of ( f(x) = (x + 1)^2 ) is ( f^{-1}(x) = \sqrt{x} - 1 ).

By signing up, you agree to our Terms of Service and Privacy Policy

- What is the end behavior of the cosine function?
- How do you identify all horizontal and slant asymptote for #f(x)=(2x^3-x^2-2x+1)/(x^2+3x+2)#?
- How do you find the horizontal asymptote for #y = x / (x-3)#?
- How do you find vertical, horizontal and oblique asymptotes for #(x^2 - 2x + 3) / x#?
- How do you determine if #xy=1# is an even or odd function?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7