Question

Let $f(x) = \sqrt{x^{4} + 15,}$ then the graph of the function $y = f(x)$ is symmetrical about

• A. The x-axis
• B. The y-axis
• C. The origin
• D. The line $x = y$

Answer 1

Answer: (B)

The y-axis

Answer 2

$f(x) = \sqrt{x^{4} + 15}$ $\Rightarrow$ $f( - x) = \sqrt{( - x)^{4} + 15}$ $= \sqrt{x^{4} + 15} = f(x)$

$\Rightarrow f( - x) = f(x) \Rightarrow f(x)$ is an even function

$\Rightarrow f(x)$ is symmetric about y-axis.