Short Quiz

Let \(f: \mathbf{R} \rightarrow \mathbf{R}\) be given by \(f(x)=\tan x\). Then \(f^{-1}(1)\) is

Assertion (A) : A function \(\mathrm{f}: \mathrm{N} \rightarrow \mathrm{N}\) given by \(\mathrm{f}(\mathrm{x})=\mathrm{x}^3+2, \forall \mathrm{x} \in \mathrm{N}\) is one-one but not onto.

Reason (R) : Since \(\forall \mathbf{y} \in \mathbf{N}\) (Codomain), there does not exist \(\mathbf{x}=(\mathbf{y}-2)^{1 / 3}\) in N (Domain) such that \(\mathrm{f}(\mathrm{x})=\mathrm{x}^3+2=\mathrm{y}\).

Let \(f: \mathbf{R} \rightarrow \mathbf{R}\) be defined by \(f(x)=x^2+1\). Then, pre-images of 17 and -3 , respectively, are

If a relation \(R\) on the set \(\{1,2,3\}\) be defined by \(R=\{(1,2)\}\), then \(R\) is