Odisha Board Solutions for Chapter: Relations and Functions, Exercise 3: Exercises- 3(c)

Find $x$ for which the value of $f\left(x\right)=x^2-4x+3$ is equal to $-1$

Find the value/values of $x$ for which the following functions are not defined:

(ii) $\frac{\sin x}{x}$

Find the value/values of $x$ for which the following functions are not defined:

(iii) $\frac{\log \cos x}{\sec x}$

If $\left(x\right)={\log }_e\left(\frac{1-x}{1+x}\right)$, then prove that $f\left(x\right)+f\left(y\right)=f\left(\frac{x+y}{1+xy}\right)$

Let $f=\left\{\left(-1,4\right),\left(2,7\right),\left(-2,11\right),\left(0,1\right),\left(1,2\right)\right\}$ be a quadratic polynomial from $Z$ to $Z$. Find $f\left(x\right)$.

Sketch the graphs of the following functions:

(i) $f\left(x\right)=x^3$.

Sketch the graphs of the following functions:  $f\left(x\right)=1+\frac{1}{x^2}$

Sketch the graphs of the following functions:

(iii) $f\left(x\right)={\left(x-1\right)}^2$