Find the inverse of the function.
-$$f ( x ) = \sqrt { x + 3 }$$
A) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = ( \mathrm { x } + 3 ) ^ { 2 }$
B) $f ^ { - 1 } ( x ) = x ^ { 2 } - 3 , x \geq 0$
C) $f ^ { - 1 } ( x ) = \sqrt { x - 3 }$
D) Not a one-to-one function

Question

Quizplus · Accepted Answer

To find the inverse of $f(x) = \sqrt{x + 3}$, we swap $x$ and $y$ and solve for $y$. This gives us $x = \sqrt{y + 3}$, which when squared on both sides becomes $x^2 = y + 3$, or $y = x^2 - 3$. The domain of the original function $f(x)$ is $x \geq -3$, which translates to the range of the inverse function being $x \geq 0$. Therefore, the correct inverse function is $f^{-1}(x) = x^2 - 3, x \geq 0$.

Find the Inverse of the Function f(x)=x+3f ( x ) = \sqrt { x + 3 }f(x)=x+3​

Find the Inverse of the Function $f ( x ) = \sqrt { x + 3 }$