Tamil Nadu Board Solutions for Chapter: Relations and Functions, Exercise 13: Exercise 1.5

Find the value of $k,$ such that $f\circ g=g\circ f$

$f\left(x\right)=3x+2, g\left(x\right)=6x-k$

Find the value of $k$ (as an improper fraction), such that $f\circ g=g\circ f$

$f\left(x\right)=2x-k, g\left(x\right)=4x+5$

If $f\left(x\right)=x^2-1, g\left(x\right)=x-2$ find $a,$ if $g\circ f\left(a\right)=1$.

Let $f\left(x\right)=x^2-1$. Find $f\circ f$

Let $f\left(x\right)=x^2-1$. Find $f\circ f\circ f$.

Consider the functions $f\left(x\right), g\left(x\right), h\left(x\right)$ as given below. Show that $(f\circ g)\circ h=f\circ (g\circ h)$.

$f\left(x\right)=x-4, g\left(x\right)=x^2$ and $h\left(x\right)=3x-5$

Let $f=\left\{\right(-1, 3), (0, -1), (2, -9\left)\right\}$ be a linear function from $Z$ into $Z$. Find $f\left(x\right)$

In electrical circuit theory, a circuit $C\left(\mathrm{t}\right)$ is called a linear circuit if it satisfies the superposition principle given by $C\left(a{t}_1+b{t}_2\right)=aC\left(t_1\right)+bC\left(t_2\right),$ where $a, b$ are constants. Show that the circuit $C\left(t\right)=3t$ is linear.