Question

For each real $x$, let $f\left(x\right)=max\{x,x^2,x^3,x^4\}$, then $f\left(x\right)$ is

• A. $x^4$ for $x\le -1$
• B. $x^2$ for $-1<x\le 0$
• C. $f\left(\frac{1}{2}\right)=\frac{1}{2}$
• D. $f\left(\frac{1}{2}\right)=\frac{1}{4}$

Answer 1

The correct option is A $x^4$ for $x\le -1$

For $x\le -1$

$f\left(x\right)=x^4$. $x$ and $x^3$ both are negative while $x^2$ is less than $x^4$

For fractional no.s lower the exponent larger is the no. But since $x$ is negative $x^2$ is the value of f(x) for given interval in Option B while $x$ is the correct answer in option c as $x$ is positive there.