Question

If the function $f: R \rightarrow R$ is given by $f(x)=x^2+3 x+1$ and $g: R \rightarrow R$ is given by $g(x)=2 x-3$, find (i) fog and (ii) gof.

Answer 1

SOLUTION : $\text { fog }=g(x)^2+3 g(x)+1 \\$

$f \circ g=4 x^2-6 x+1 \\$

$g \circ f=2\left(x^2+3 x+1\right)-3$

$\text { fog }=(2 x-3)^2+3(2 x-3)+1 \\$

$\text { gof }=2 f(x)-3 \\$

$\text { gof }=2 x^2+6 x-1$