If $f(x)=\left[4-(x-7)^3\right]$, then $f^{-1}(x)=$ ............ .
Given that,
$$\begin{aligned} f(x) & =\left\{4-(x-7)^3\right\} \\ \text{Let}\quad y & =\left[4-(x-7)^3\right] \end{aligned}$$
$(x-7)^3=4-y$
$(x-7)=(4-y)^{1 / 3}$
$\Rightarrow\quad x=7+(4-y)^{1 / 3}$
$f^{-1}(x)=7+(4-x)^{1 / 3}$
Let $R=\{(3,1),(1,3),(3,3)\}$ be a relation defined on the set $A=\{1,2,3\}$. Then, $R$ is symmetric, transitive but not reflexive.
If $f: R \rightarrow R$ be the function defined by $f(x)=\sin (3 x+2) \forall x \in R$. Then, $f$ is invertible.
Every relation which is symmetric and transitive is also reflexive.
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