Question

find $(f \circ g)(x)$ for the functions $f(x) = \sqrt{2x} + 5$ and $g(x) = 3x - 4$.

select one:
\\( \bigcirc \\) a. \\( (f \circ g)(x) = \sqrt{6x + 8} + 5 \\)
\\( \bigcirc \\) b. \\( (f \circ g)(x) = \sqrt{6x - 8} - 5 \\)
\\( \bigcirc \\) c. \\( (f \circ g)(x) = \sqrt{6x - 8} + 5 \\)
\\( \bigcirc \\) d. \\( (f \circ g)(x) = 3\sqrt{2x} + 11 \\)

Explanation:

Step1: Define function composition

$(f \circ g)(x) = f(g(x))$

Step2: Substitute $g(x)$ into $f(x)$

Replace $x$ in $f(x)$ with $g(x)=3x-4$:
$f(g(x)) = \sqrt{2(3x-4)} + 5$

Step3: Simplify the radicand

Calculate $2(3x-4)$:
$\sqrt{6x - 8} + 5$

Answer:

C. $(f \circ g)(x) = \sqrt{6x - 8} + 5$