MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Rational Function

If fx=x+1x, x...

Question

If $f (x) = x + \frac{1}{x}, x \neq 0; then {(f (x)]}^{3} =$

A

f (x^{3}) + 3 f (x)

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

B

f (x^{3}) - 3 f (x)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

C

f (x^{3}) + 3 f (\frac{1}{x})

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

D

f (x^{3}) - 3 f (\frac{1}{x})

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $f (x^{3}) + 3 f (\frac{1}{x})$
$f (x) = x + \frac{1}{x} f (x^{3}) = x^{3} + \frac{1}{x^{3}} {(f (x)]}^{3} = {(x + \frac{1}{x})}^{3} = x^{3} + \frac{1}{x^{3}} + 3 (x + \frac{1}{x}) \Rightarrow {(f (x)]}^{3} = f (x^{3}) + 3 f (x) f (\frac{1}{x}) = \frac{1}{x} + x = f (x) ∴ {(f (x)]}^{3} = f (x^{3}) + 3 f (\frac{1}{x})$

Suggest Corrections

thumbs-up

0

Similar questions

f (x) = x + \frac{1}{x}, x \neq 0; then {(f (x)]}^{3} =

f (x) = x - \frac{1}{x}

then prove that

{(f (x))}^{3} = f (x^{3}) + 3 f (\frac{1}{x})

f (x) = {\begin{matrix} 1 & x < 0 x^{2} & x \geq 0 \end{matrix}

x = 0

f (x) = x + (1 / x)

{f (x)}^{3} = f (x^{3}) + 3 f (1 / x)

f (x) = x + \frac{1}{x}

[f (x)]^{3} = f (x^{3}) + 3 f (\frac{1}{x})

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Some Functions and Their Graphs

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Rational Function

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon