The function f(x)=x2−1 is reflected over the y-axis. Choose the equation that correctly identifies g(x) .

Question

A. g(x)=−x^2+1
B. g(x)=−x^2−2
C. g(x)=x^2−1
D. g(x)=x^2+1

Answer 1

To reflect the function \( f(x) = x^2 - 1 \) over the y-axis, we replace \( x \) with \( -x \) in the function.

Thus, the reflection is:

\[ g(x) = f(-x) = (-x)^2 - 1 \]

Calculating this gives:

\[ g(x) = x^2 - 1 \]

So the correct choice is:

C. g(x) = x^2 - 1