Question

If f, g : R → R be defined by f(x) = 2x + 1 and g(x) = x2 - 2, ∀ x ∈ R, respectively . Then, find fog

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{fog(x)=2x^{2}-3}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given: }} \\ \tt: \implies f(x) = 2x + 1 \\ \\ \tt: \implies g(x) = {x}^{2} - 2 \\ \\ \red{\underline \bold{To \: Find: }} \\ \tt: \implies fog(x)=?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies fog(x) = f(g(x)) \\ \\ \tt: \implies fog(x) = f( {x}^{2} - 2) \\ \\ \tt: \implies fog(x) = 2( {x}^{2} - 2) + 1 \\ \\ \tt: \implies fog(x)= {2x}^{2} - 4 + 1 \\ \\ \green{\tt: \implies fog(x) = 2 {x}^{2} - 3} \\ \\ \green{\tt \therefore fog(x) \: is \: {2x}^{2} - 3}$