R S Aggarwal Solutions for Exercise 3: EXERCISE

Let $f : R \to R$and $g : R \to R$ defined by $f\left(x\right)=x^2$ and $g\left(x\right) = (x + 1).$ Show that $g \circ f \ne f \circ g.$

Let $f:R\to R:f\left(x\right)={\left(3-x^3\right)}^{1/3}$. Find $f\circ f.$

Let $f : R \to R : f\left(x\right) = 3x + 2$, find $f\left(f\left(x\right)\right)$.

Let $f=\left\{\right(1,2),(3,5),(4,1)\}$ and $g=\{(1,3),(2,3),(5,1))$. Write down $g o f$.

Let $A=\{1,2,3,4\}$ and $f=\left\{\right(1,4),(2,1\left)\right(3,3),(4,2)\}$. Write down $(f o f).$

Let $f\left(x\right)=8x^3$and $g\left(x\right)=x^{1/3}$. Find $g o f$and $f o g$.

Let $f : R \to R : f\left(x\right) = 10x + 7.$ Find the function $g:R\to R:gof=fog=I_g$.

Let $A=\{1,2,3\},B=\{4,5,6,7\}$ and let $f=\left\{\right(1,4),(2,5),(3,6)\}$ be a function from $A$to $B$. State whether $f$is one-one.