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