If f(x) = 4 x^3 + 3 x^2 + 3x + 4, then x^3 f ( 1 x ) is - Vidyadip

MCQ

If $f(x) = 4{x^3} + 3{x^2} + 3x + 4$, then ${x^3}f\left( {\frac{1}{x}} \right)$ is

A
$f( - x)$
B
$\frac{1}{{f(x)}}$
C
${\left( {f\left( {\frac{1}{x}} \right)} \right)^2}$
✓
$f(x)$

✓

Answer

Correct option: D.

$f(x)$

d
(d) ${x^3}f\left( {\frac{1}{x}} \right) = {x^3}\,\left[ {\frac{4}{{{x^3}}} + \frac{3}{{{x^2}}} + \frac{3}{x} + 4} \right]$

$ = 4 + 3x + 3{x^2} + 4{x^3} = f(x)$.

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