Questions: For f(x)=4x and g(x)=x+2, find the following functions: a. (f ∘ g)(x); b. (g∘ /)(x); c. (f∘ g)(2); d. (9∘ 0)(2).

Transcript text: For $f(x)=4 x$ and $g(x)=x+2$, find the following functions: a. $(f \circ g)(x)$; b. $\left(g^{\circ} /(x)\right.$; c. $\left(f^{\circ} \mathrm{g}\right)(2)$; d. $\left(9^{\circ} 0\right)(2)$.

Solution

Solution Steps

Step 1: Finding the composition $(f \circ g)(x)$

First, evaluate $g(2) = 4$. Then, substitute this into $f(x)$ to get $f(g(2)) = 16$. After simplification, $(f \circ g)(2) = 16$.

Step 2: Finding the composition $(g \circ f)(x)$

First, evaluate $f(2) = 8$. Then, substitute this into $g(x)$ to get $g(f(2)) = 10$. After simplification, $(g \circ f)(2) = 10$.

Final Answer:

The composition $(f \circ g)(2)$ is approximately 16 when rounded to 2 decimal places. The composition $(g \circ f)(2)$ is approximately 10 when rounded to 2 decimal places.

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