Tamil Nadu Board Solutions for Chapter: Relations and Functions, Exercise 7: Exercise 1.3

A graph representing the function $f\left(x\right)$ is given in figure, it is clear that $f\left(9\right)=2$.

Describe the Range.

A function $f$ is defined by $f\left(x\right)=2x-3$, find $x$ such that $f\left(x\right)=0$.

A function $f$ is defined by $f\left(x\right)=2x-3$. Find $x$ such that $f\left(x\right)=x$.

A function $f$ is defined by $f\left(x\right)=2x-3$

find $x$ such that $f\left(x\right)=f(1-x)$

A function $f$ is defined by $f\left(x\right)=3-2x$. Find $x$ such that $f\left(x^2\right)=\left(f\right(x){)}^2$

A plane is flying at a speed of $500 \mathrm{km}$ per hour. Express the distance $d$ travelled by the plane as function of time $t$ in hours. 

The data in the adjacent table depicts the length of a woman’s forehand and her corresponding height. Based on this data, a student finds a relationship between the height $\left(y\right)$ and the forehand length $\left(x\right)$ as $y=ax+b$ where $a, b$ are constants.  

 The height of a woman is $K$ inches whose forehand length is $40 \mathrm{cm}.$ Find the value for $K$.

The data in the adjacent table depicts the length of a woman’s forehand and her corresponding height. Based on this data, a student finds a relationship between the height $\left(y\right)$ and the forehand length $\left(x\right)$ as $y=ax+b$ where $a, b$ are constants.  

The given height of woman is $53.3$ inches.  If the length of forehand of a woman is $k \mathrm{cm}$, find the value of $k$.