Respuesta :
[tex]\bf \begin{cases}
f(x)=\sqrt{x+9}\\\\
g(x)=8x+13
\end{cases}\qquad (f\circ g)(x)\iff f(\ g(x)\ )=\sqrt{\boxed{g(x)}+9}
\\\\\\
thus\qquad f(\ g(x)\ )=\sqrt{\boxed{8x+13}+9}[/tex]
simplify it away
simplify it away
Answer:
The answer will be : [tex]2\sqrt{2x-1}[/tex]
Step-by-step explanation:
f(x) = Square root of quantity x plus nine.
Mathematically we can write this as:
[tex]f(x)=\sqrt{x+9}[/tex]
[tex]g(x)=8x-13[/tex]
Now, we have to find [tex]f(g(x))[/tex]
So, we will replace x in f(x) with : 8x-13.
[tex]f(g(x))=f(8x-13)[/tex]
= [tex]\sqrt{8x-13+9}[/tex]
= [tex]\sqrt{8x-4}[/tex]
= [tex]\sqrt{4(2x-1)}[/tex]
= [tex]2\sqrt{2x-1}[/tex]
Hence, answer is : f(g(x)) = [tex]2\sqrt{2x-1}[/tex]
