The inverse of the function is f x -10 x -10- x -10 x -10- x -1 isA- f -1 x -log 10 x -2- xB- f -1 x -1-2log 10 x -2- xC- f -1 x -1-2log 10 x -1- xD- None of these

The correct option is B f^ 1(x)=1/2log_10x/2 xLet f(x) = y ⇒10^x 10^ x/10^x+10^ x+1=y Applying componendo and divendo ⇒ x=1/2 log_10y/2 y⇒ f^ 1(x)=1/2 log_1 ...

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Byju's Answer

Standard IX

Mathematics

How to Find the Inverse of a Function

The inverse o...

Question

The inverse of the function is $f (x) = \frac{10^{x} - 10^{- x}}{10^{x} + 10^{- x}} + 1$ is

f^{- 1} (x) = l o g_{10} \frac{x}{2 - x}

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f^{- 1} (x) = \frac{1}{2} l o g_{10} \frac{x}{2 - x}

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f^{- 1} (x) = \frac{1}{2} l o g_{10} \frac{x}{1 - x}

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Solution

The correct option is B $f^{- 1} (x) = \frac{1}{2} l o g_{10} \frac{x}{2 - x}$
Let f(x) = y
$\Rightarrow \frac{10^{x} - 10^{- x}}{10^{x} + 10^{- x}} + 1 = y$
Applying componendo and divendo -
$\Rightarrow x = \frac{1}{2} l o g_{10} \frac{y}{2 - y} \Rightarrow f^{- 1} (x) = \frac{1}{2} l o g_{10} \frac{x}{2 - x}$

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Similar questions

Q. The inverse of the function is

f (x) = \frac{10^{x} - 10^{- x}}{10^{x} + 10^{- x}} + 1

Q. If

f : R \to (- 1, 1)

is defined by

f (x) = \frac{- x | x |}{1 + x^{2}}, then f^{- 1} (x)

equals
(a)

\sqrt{\frac{|x|}{1 - |x|}}

(b)

S g n (x) \sqrt{\frac{|x|}{1 - |x|}}

(c)

- \sqrt{\frac{x}{1 - x}}

(d) None of these

Q. Let

A = \{x \in R : x \leq 1\} and f : A \to A

be defined as

f (x) = x (2 - x)

. Then,

f^{- 1} (x)

is
(a)

1 + \sqrt{1 - x}

(b)

1 - \sqrt{1 - x}

(c)

\sqrt{1 - x}

(d)

1 \pm \sqrt{1 - x}

f : [2, \infty) \to (- \infty, 4], w h e r e f (x) = x (4 - x) t h e n f^{- 1} (x) i s

Q. If the function

f : R \to R

be such that

f (x) = x - [x]

, where [x] denotes the greatest integer less than or equal to x, then

f^{- 1} (x)

is

(a)

\frac{1}{x - [x]}

(b) [x] − x

(c) not defined

(d) none of these

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The inverse of the function is f(x)=10x−10−x10x+10−x+1 is

The correct option is B f−1(x)=12log10x2−xLet f(x) = y ⇒10x−10−x10x+10−x+1=y Applying componendo and divendo - ⇒x=12 log10y2−y⇒f−1(x)=12 log10 x2−x

The inverse of the function is $f (x) = \frac{10^{x} - 10^{- x}}{10^{x} + 10^{- x}} + 1$ is