What is Multiplicative Inverse?

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ALOK_RAJ Asked Aug 14, 2023

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Let $f: N \rightarrow Y$ be a function defined as $f(x)=4 x+3$, where $Y=\{y \in N: y=4 x+3$ for some $x \in N\}$. Show that $f$ is invertible. Find the inverse.

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Let $y=\left\{n^2: n \in N\right\}$ Consider $f: N \rightarrow y$ as $f(n)=n^2$. Show that $f$ is invertible. Find the inverse of $f$.

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If $g$ is the inverse of a function $f$ and $f^{\prime}(x)=\frac{1}{1+x^5}$, then $g^{\prime}(x)$ equal to:

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Let $f: N \rightarrow Y$ be a function defined as $f(x)=4 x+3$ where $Y=\{y \in N: y=4 x+3$ for some $x \in N\}$. Its inverse is -

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Show that $-{a}$ is not the inverse of ${a} \in {N}$ for the addition operation + on ${N}$ and $\frac{1}{{a}}$ is not the inverse of $a \in {N}$ for multiplication operation $\times$ on ${N}$ for ${a} \neq 1$.

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Given a binary operation $: A \times A \rightarrow A$ with the identity element $e$ in $A$, an element $a \in A$ is said to be invertible with respect to the operation * if there exists an element $b$ in A such that $a^* b=e=b^* a$ and $b$ is called the inverse of $a$ and is denoted by ${a}^{-1}$.

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