If f(x)=3x+2 and g(x)=√2x+5, then find (fog) (1)

1.	If f(x)=3x+2 and g(x)=√2x+5, then find (fog) (1)
Answer» $\blue{\bold{\underline{\underline{Answer:}}}}$ $\green{\tt{\therefore{fog(1)=3\sqrt{2}+17}}}$ $\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$ $\green{\underline \bold{<klux>GIVEN</klux>: }} \\ \tt: \implies f(x) = 3x + 2\\ \\ \tt: \implies g(x) = \sqrt{2}{x}+5 \\ \\ \red{\underline \bold{To \: Find: }} \\ \tt: \implies fog(1)=?$ • ACCORDING to given QUESTION : $\bold{As \: we \: know \: that} \\ \tt: \implies fog(x) = f(g(x)) \\ \\ \tt: \implies fog(x) = f( \sqrt{2}x + 5) \\ \\ \tt: \implies fog(x) = 3(\sqrt{2}x + 5) + 2 \\ \\ \tt: \implies fog(x)= 3\sqrt{2}x+15+2 \\ \\ \green{\tt: \implies fog(x) = 3\sqrt{2}x+17}$ $\tt: \implies fog(1) = 3\sqrt{2} \times 1 + 17 \\ \\ \green{\tt: \implies fog(1) = 3 \sqrt{2} + 17} \\ \\ \green{\tt \therefore \tt: \implies fog(1) \: is \: 3 \sqrt{2} + 17}$

Answer»

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

$\green{\tt{\therefore{fog(1)=3\sqrt{2}+17}}}$

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

$\green{\underline \bold{<klux>GIVEN</klux>: }} \\ \tt: \implies f(x) = 3x + 2\\ \\ \tt: \implies g(x) = \sqrt{2}{x}+5 \\ \\ \red{\underline \bold{To \: Find: }} \\ \tt: \implies fog(1)=?$

• ACCORDING to given QUESTION :

$\bold{As \: we \: know \: that} \\ \tt: \implies fog(x) = f(g(x)) \\ \\ \tt: \implies fog(x) = f( \sqrt{2}x + 5) \\ \\ \tt: \implies fog(x) = 3(\sqrt{2}x + 5) + 2 \\ \\ \tt: \implies fog(x)= 3\sqrt{2}x+15+2 \\ \\ \green{\tt: \implies fog(x) = 3\sqrt{2}x+17}$

$\tt: \implies fog(1) = 3\sqrt{2} \times 1 + 17 \\ \\ \green{\tt: \implies fog(1) = 3 \sqrt{2} + 17} \\ \\ \green{\tt \therefore \tt: \implies fog(1) \: is \: 3 \sqrt{2} + 17}$

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