CameraIcon

SearchIcon

MyQuestionIcon

1

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

How to Find the Inverse of a Function

If fx=2+x3,...

Question

If $f (x) = 2 + x^{3}$ , then $f^{- 1} (x)$ is equal to

A

\sqrt[3]{x} + 2

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

B

\sqrt[3]{x} - 2

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

C

\sqrt[3]{x - 2}

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

D

\sqrt[3]{x + 2}

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

Open in App

Solution

The correct option is D $\sqrt[3]{x - 2}$
Let $f (x) = y$
$\Rightarrow 2 + x^{3} = y$
$\Rightarrow x^{3} = y - 2$
$\Rightarrow x = {(y - 2)}^{1 / 3}$
$∴ f^{- 1} (y) = x$ $= {(y - 2)}^{1 / 3}$
$∴ f^{- 1} (x) = {(x - 2)}^{1 / 3}$

Suggest Corrections

thumbs-up

0

Similar questions

f (x) = - 4 e^{\frac{1 - x}{2}} + 1 + x + \frac{x^{2}}{2} + \frac{x^{3}}{3}

g (x) = f^{- 1} (x)

then the reciprocal of

g^{'} (\frac{- 7}{6})

f (x) = {\begin{matrix} x^{3} + 1, & x < 0 x^{2} + 1, & x \geq 0 \end{matrix}, g (x) = ⎧ ⎨ ⎩ \begin{matrix} (x - 1)^{\frac{1}{3}}, & x < 1 (x - 1)^{\frac{1}{2}}, & x \geq 1 \end{matrix}

then (gof) (x) is equal to

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

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

is equal to

(a) 2x³

(b)

\frac{2}{x^{3}}

f (x) = \log_{e} (\frac{1 + x}{1 - x})

f (\frac{2 x}{1 + x^{2}})

is equal to

(a) [f(x)]²
(b) [f(x)]³
(c) 2f(x)
(d) 3f(x)

x = \frac{1}{2 - \sqrt{3}}

x^{3} - 3 (x - 1) (x + 2) =

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Inverse of a Function

MATHEMATICS

Watch in App

explore_more_icon

Explore more

How to Find the Inverse of a Function

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon