Question

Please just verify my answers, I'm really paranoid about messing up.

Answer 1

Given

$\begin{gathered} f(x)=x^2 \\ g(x)=-f(-x) \end{gathered}$

To find: The correct options.

Explanation:

It is given that,

$\begin{gathered} f(x)=x^2 \\ g(x)=-f(-x) \end{gathered}$

That implies,

$\begin{gathered} f(x)=x^2 \\ g(x)=-f(-x) \\ =-(-x)^2 \\ =-x^2 \end{gathered}$

Then,

f(-x) is even.

So, g(x) = -f(-x) is even.

Hence, g(x) is even.

Also,

$\begin{gathered} g\mleft(x\mright)=-f\mleft(-x\mright) \\ \end{gathered}$

Then, g(x) is the reflection of f(x) over both the axes.

Hence, options a), c), d) are correct.