Question

If the functions f:R$\to$ R and g:R$\to$ R be defined by f(x)=$2x+1,g\left(x\right)=x^2-2$. Find the formulae for g o f and f o g.
Is g o f = f o g.$.

• A. True
• B. False

Answer 1

The correct option is B False

Given, $f\left(x\right)=2x+1$
$g\left(x\right)=x^2-2$
$f\left(g\right(x\left)\right)=(2x+1{)}^2-2$
$=4x^2+4x-1$ ...(i)
$g\left(f\right(x\left)\right)=2(x^2-2)+1$
From (i) and (ii),

$fog\ne gof$