Question

If $f\left(x\right)=x^4+5x^2+1$, then $f\left(\frac{1}{x}\right)=$

• A. $\frac{f\left(x\right)}{x^4}$
• B. $\frac{f\left(x\right)}{x^3}$
• C. $x^{2}f\left(x\right)$
• D. $x^{4}f\left(x\right)$

Answer 1

The correct option is A $\frac{f\left(x\right)}{x^4}$

Given $f\left(x\right)=x^4+5x^2+1$
Now, $f\left(\frac{1}{x}\right)=\frac{1}{x^4}+\frac{5}{x^2}+1$
$=\frac{1+5x^2+x^4}{x^4}$
$=\frac{f\left(x\right)}{x^4}$
$\Rightarrow f\left(\frac{1}{x}\right)=\frac{f\left(x\right)}{x^4}$