Question

which equation can be simplified to find the inverse of $y = x^2 - 7$?
\\(\circ\\) $x = y^2 - \frac{1}{7}$
\\(\circ\\) $\frac{1}{x} = y^2 - 7$
\\(\circ\\) $x = y^2 - 7$
\\(\circ\\) $-x = y^2 - 7$

Explanation:

Step1: Recall inverse function steps

To find the inverse of a function \( y = f(x) \), we swap \( x \) and \( y \) and then solve for \( y \).

Step2: Apply to given function

Given the function \( y = x^2 - 7 \), to find its inverse, we first swap \( x \) and \( y \). This gives us \( x = y^2 - 7 \).

Answer:

C. \( x = y^2 - 7 \) (assuming the third option is labeled C; if the original labels were different, adjust the label but keep the equation \( x = y^2 - 7 \))