Find the inverse of the function.
-$$f ( x ) = 7 x ^ { 2 } + 7 , x \geq 0$$
A) $f ^ { - 1 } ( x ) = \sqrt { \frac { x - 7 } { 7 } }$
B) Not a one-to-one function
C) $f ^ { - 1 } ( x ) = \frac { 7 } { \sqrt { x } - 7 }$
D) $f ^ { - 1 } ( x ) = \sqrt { \frac { 7 } { x - 7 } }$

Question

Quizplus · Accepted Answer

To find the inverse, solve for $x$ in terms of $y$: $y = 7x^2 + 7$. Subtract 7 from both sides, divide by 7, then take the square root, considering $x \geq 0$, to get $x = \sqrt{\frac{y-7}{7}}$. Replace $x$ with $f^{-1}(x)$ and $y$ with $x$ to get $f^{-1}(x) = \sqrt{\frac{x-7}{7}}$.

Find the Inverse of the Function f(x)=7x2+7,x≥0f ( x ) = 7 x ^ { 2 } + 7 , x \geq 0f(x)=7x2+7,x≥0

Find the Inverse of the Function $f ( x ) = 7 x ^ { 2 } + 7 , x \geq 0$