First slide

Algebra of real valued functions

Question

If f(x)=4x³+3x²+3x+4,then x³f(1/x)

Moderate

A

f(-x)
B

1/f(x)
C

${[f (\frac{1}{x})]}^{2}$
D

f(x)

Solution

we have
f(x)=4x³+3x²+3x+4
$\Rightarrow f (\frac{1}{x}) = \frac{4}{x^{3}} + \frac{3}{x^{2}} + \frac{3}{x} + 4 \Rightarrow x^{3} f (\frac{1}{x}) = x^{3} (\frac{4}{x^{3}} + \frac{3}{x^{2}} + \frac{3}{x} + 4) = 4 + 3 x + 3 x^{2} + 4 x^{3} ∴ x^{3} f (\frac{1}{x}) = f (x)$

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