Question

f(x)=x-6, g(x)=x² find fog and gof​

Answer 1

${\large{\underline{\underline{\text{\red{Given :}}}}}}$

$f(x)=x-6 , \:\: g(x)=x^2$

${\large{\underline{\underline{\text{\red{To Find :}}}}}}$

$fog \:\: {\text{and}}\:\: gof$

${\large{\underline{\underline{\text{\red{Solution :}}}}}}$

$(i) fog$

$\implies fog \implies f(g(x))$

$\implies f(g(x)) \implies f(x^2)$

$\implies f(x^2)\implies x^2-6$

${\red{fog = x^2-6}}$

$(ii) gof$

$\implies gof \implies g(f(x))$

$\implies g(f(x))\implies g(x-6)$

$\implies g(x-6)=(x-6)^2$

${\red{gof=(x-6)^2}}$