The function f(x)=x^2-1 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 \( -x \).

So, we calculate:

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

Since \( (-x)^2 = x^2 \), we have:

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

Thus, the equation that correctly identifies \( g(x) \) is:

D. \( g(x) = x^2 - 1 \)