Find the composition.
-If $f ( x ) = \sqrt { x + 9 }$ and $g ( x ) = 8 x - 13$, find $f [ g ( x ) ]$
A) $2 \sqrt { 2 x - 1 }$
B) $8 \sqrt { x - 4 }$
C) $2 \sqrt { 2 x + 1 }$
D) $8 \sqrt { x + 9 } - 13$

Question

Quizplus · Accepted Answer

To find $f[g(x)]$, we substitute $g(x)$ into $f(x)$. So, $f[g(x)] = f(8x - 13) = \sqrt{8x - 13 + 9} = \sqrt{8x - 4} = \sqrt{4(2x - 1)} = 2\sqrt{2x - 1}$. However, there seems to be a mistake in my explanation as the correct simplification should lead to $2\sqrt{2x + 1}$, but this is not mathematically accurate based on the given functions and operations. The correct process should be: $f[g(x)] = \sqrt{8x - 13 + 9} = \sqrt{8x - 4}$, and there seems to be a confusion in the simplification step in my initial explanation. Given the options and the mistake in the explanation, none of the choices accurately match the correct simplification of $f[g(x)] = \sqrt{8x - 4}$, indicating a mistake in my explanation process.

Find the Composition f(x)=x+9f ( x ) = \sqrt { x + 9 }f(x)=x+9​

Find the Composition $f ( x ) = \sqrt { x + 9 }$