Question

If $f\left(x\right)f\left(\frac{1}{x}\right)=f\left(x\right)+f\left(\frac{1}{x}\right)\forall xϵR-0$ where f(x) be a polynomial function and f(5) =126 then f(3)=

• A. 28
• B. 26
• C. 27
• D. 25

Answer 1

The correct option is A 28

$f\left(x\right)=1\pm x^{n}or,f\left(5\right)=1\pm 5^n$
or,$126=\pm 5^n$
or,$\pm 5^n=125\Rightarrow \pm 5^n=5^3$
n=3
$f\left(3\right)=1+3^3=28$