Question

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

Answer 1

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This is a composition of functions

f(x)=2x+5

g(x)=3+x

[fog](x)=f(g(x))=f(3+x)=2(3+x)+5

=6+2x+5=2x+11

And

[gof](x)=g(f(x))=g(2x+5)=3+2x+5

= 2x + 8

Hopes it help you✌️✌️

Answer 2

❥$\:{\red{\underline{\underline{\large{\mathtt{GIVEN}}}}}}$

• f(x) = 3x + 2
• g(x) = √2x + 5

❥$\:{\orange{\underline{\underline{\large{\mathtt{TO\:FIND}}}}}}$

• fog(1)

❥$\:{\purple{\underline{\underline{\large{\mathtt{SOLUTION}}}}}}$

⇒ fog(x) = f(g(x))

⇒ fog(x) = f(√2x + 5)

⇒ fog(x) = 3(√2x + 5)+2

⇒ fog(x) = 3√2x + 15 + 2

⇒ fog(x) = 3√2x + 17

⇒ fog(1) = 3√2 × 1 + 17

⇒ fog(1) = 3√2 + 17

★ Hence, fog(1) is 3√2 + 17