Respuesta :
Answer:
[tex]g(x)=x+\frac{1}{9}+\frac{2\sqrt{x}}{3}[/tex]
Step-by-step explanation:
Given functions: h(x) = (fog)(x) , h(x) = 3√x + 3 and f(x) = 3√x + 2
To find: function g(x)
Consider,
(fog)(x) = h(x)
f( g(x) ) = h(x)
[tex]3\sqrt{g(x)}+2=3\sqrt{x}+3[/tex]
[tex]3\sqrt{g(x)}=3\sqrt{x}+1[/tex]
[tex]\sqrt{g(x)}=\frac{3\sqrt{x}+1}{3}[/tex]
[tex]\sqrt{g(x)}=\sqrt{x}+\frac{1}{3}[/tex]
[tex]g(x)=(\sqrt{x}+\frac{1}{3})^2[/tex]
[tex]g(x)=(\sqrt{x})^2+(\frac{1}{3})^2+2\times\frac{1}{3}\times\sqrt{x}[/tex]
[tex]g(x)=x+\frac{1}{9}+\frac{2\sqrt{x}}{3}[/tex]
Therefore, [tex]g(x)=x+\frac{1}{9}+\frac{2\sqrt{x}}{3}[/tex]
Answer:
[tex]g(x)=x+1[/tex]
Step-by-step explanation:
Consider the functions
[tex]h(x)=3\sqrt{x+3}[/tex]
[tex]f(x)=3\sqrt{x+2}[/tex]
It is given that
[tex]h(x)=(f\circ g)(x)[/tex]
Using the composition of functions, we get
[tex]h(x)=f(g(x))[/tex]
[tex]3\sqrt{x+3}=3\sqrt{(g(x)+2}[/tex] [tex][\because h(x)=3\sqrt{x+3}, f(x)=3\sqrt{x+2}][/tex]
Divide both sides by 3.
[tex]\sqrt{x+3}=\sqrt{(g(x)+2}[/tex]
Taking square on both sides.
[tex]x+3=g(x)+2[/tex]
Subtract 2 from both sides.
[tex]x+3-2=g(x)[/tex]
[tex]x+1=g(x)[/tex]
Interchange the sides.
[tex]g(x)=x+1[/tex]
Therefore, the required function is g(x)=x+1.
