Question

find ((f circ g)(4)) for the following functions. round your answer to two decimal places, if necessary. (f(x) = sqrt{\frac{4x}{3}}) and (g(x) = 2 + sqrt{x})
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((f circ g)(4) = square)

Explanation:

Step1: Calculate g(4) first

$g(4) = 2 + \sqrt{4} = 2 + 2 = 4$

Step2: Substitute g(4) into f(x)

$(f \circ g)(4) = f(g(4)) = f(4) = \sqrt{\frac{4 \times 4}{3}}$

Step3: Simplify the expression

$\sqrt{\frac{16}{3}} = \frac{4}{\sqrt{3}} \approx \frac{4}{1.732} \approx 2.31$

Answer:

2.31