(B) function $f: A \to B$ is invertible if and only if it is both one-one (injective) and onto (surjective). Given $f = \{(1,2), (2,1), (3,1)\}$,we ob

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(B) function $f: A \to B$ is invertible if and only if it is both one-one (injective) and onto (surjective). Given $f = \{(1,2), (2,1), (3,1)\}$,we observe the values: $f(1) = 2$ $f(2) = 1$ $f(3) = 1$ Since $f(2) = f(3) = 1$ but $2 \neq 3$,the function is not one-one. Because the function is not one-one,it cannot be invertible. Therefore,the correct answer is that $f$ is not invertible.

Class 12 Mathematics Relation and Function Inverse Function

Easy

Consider the function $f = \{(1,2), (2,1), (3,1)\}$. Is $f$ invertible?

A
Yes,$f$ is invertible.
B
No,$f$ is not invertible.
C
Yes,$f$ is invertible and $f^{-1} = f$.
D
None of these.

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Relation and Function

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Inverse Function

Let $g(x)$ be the inverse of the function $f(x)$ and $f'(x) = \frac{1}{1 + x^3}$. Then $g'(x)$ is equal to

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Let $f: R \rightarrow R$ be defined by $f(x) = 2x + 6$,which is a bijective mapping. Then $f^{-1}(x)$ is given by:

EasyKCET 2016

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If the functions $f$ and $g$ are defined by $f(x) = 3x - 4$ and $g(x) = 2 + 3x$ for $x \in R$,then $g^{-1}(f^{-1}(5))$ is equal to

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State with reason whether the following function has an inverse: $g : \{5, 6, 7, 8\} \rightarrow \{1, 2, 3, 4\}$ with $g = \{(5, 4), (6, 3), (7, 4), (8, 2)\}$.

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If $f:[1, +\infty) \to [2, +\infty)$ is given by $f(x) = x + \frac{1}{x}$,then ${f^{-1}}(x)$ equals:

MediumIIT 2001

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Consider the function $f = \{(1,2), (2,1), (3,1)\}$. Is $f$ invertible?

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Let $g(x)$ be the inverse of the function $f(x)$ and $f'(x) = \frac{1}{1 + x^3}$. Then $g'(x)$ is equal to

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