Let A- x- R-x- 0 - A function f-A- A is defined by fx- x 2- Which one of the following is correct-

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Standard XII

Mathematics

How to Find the Inverse of a Function

Let A= x∈ R...

Question

Let $A = {x \in R | x \geq 0}$ . A function $f : A \to A$ is defined by $f (x) = x^{2}$ . Which one of the following is correct?

The function does not have inverse

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f

is its own inverse

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The function has an inverse but

f

is not its own inverse

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None of the above

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Solution

The correct option is C The function has an inverse but $f$ is not its own inverse
$f (x) = x^{2} ⟹ f^{- 1} (x) = \sqrt{x}$
Clearly, $f^{- 1} (x)$ exists in the domain of definition of $f$ .
Also, $f (x)$ is not its own inverse.
Option C is the answer.

Suggest Corrections

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Let A={x∈R|x≥0}. A function f:A→A is defined by f(x)=x2. Which one of the following is correct?

The correct option is C The function has an inverse but f is not its own inversef(x)=x2⟹f−1(x)=√xClearly, f−1(x) exists in the domain of definition of f.Also, f(x) is not its own inverse.Option C is the answer.

Let $A = {x \in R | x \geq 0}$ . A function $f : A \to A$ is defined by $f (x) = x^{2}$ . Which one of the following is correct?

The correct option is C The function has an inverse but $f$ is not its own inverse
$f (x) = x^{2} ⟹ f^{- 1} (x) = \sqrt{x}$
Clearly, $f^{- 1} (x)$ exists in the domain of definition of $f$ .
Also, $f (x)$ is not its own inverse.
Option C is the answer.