Determine whether the function has an inverse function.If it does,find the inverse function. ? F(x)= (x + 4)²,x ? -4 ? A) $f ^ { - 1 } ( x ) = \sqrt { x } + 4$ B)f^-1(x)= -(x + 4)² C)f^-1(x)= (x + 4)^-2 D)? $f ^ { - 1 } ( x ) = \sqrt { x } - 4$ E)No inverse

Question

Quizplus · Accepted Answer

The function $F(x) = (x + 4)^2, x \geq -4$ is a one-to-one function on the domain $x \geq -4$, so it has an inverse. To find the inverse, replace $F(x)$ with $y$, then solve for $x$: $y = (x + 4)^2$. Taking the square root of both sides gives $x = \sqrt{y} - 4$, so the inverse function is $f^{-1}(x) = \sqrt{x} - 4$.

Determine Whether the Function Has an Inverse Function f−1(x)=x+4f ^ { - 1 } ( x ) = \sqrt { x } + 4f−1(x)=x​+4

Determine Whether the Function Has an Inverse Function $f ^ { - 1 } ( x ) = \sqrt { x } + 4$