Tamil Nadu Board Solutions for Chapter: Sets, Relations and Functions, Exercise 5: Exercise

The number of constant functions from a set containing $m$ elements to a set containing $n$ elements is

The function $f:[0,2\pi ]\to [-1,1]$ defined by $f\left(x\right)=\sin x$ is

If the function $f : \left[-3,3\right] \to S$ defined by $f\left(x\right)=x^2$ is onto, then $S$ is

Let $X=\{1,2,3,4\},Y=\{a,b,c,d\}$ and $f=\left\{\right(1,a),(4,b),(2,c),(3,d),(2,d\left)\right\}.$ Then $f$ is

The inverse of $f\left(x\right)=\left\{\begin{array}{ll}x& \text{ if }x<1\\ x^2& \text{ if } 1\le x\le 4\\ 8\sqrt{x}& \text{ if }x>4\end{array}\right.$is

Let $f:R\to R$ be defined by $f\left(x\right)=1-\left|x\right|$. Then the range of $f$ is

The function $f:R\to R$ is defined by $f\left(x\right)=\sin x+\cos x$ is

The function $f:R\to R$ defined by $f\left(x\right)=\frac{\left(x^2+\cos x\right)\left(1+x^4\right)}{(x-\sin x)\left(2x-x^3\right)}+e^{-\left|x\right|}$ is