Questions: Given the functions: f(x)=x^3+3 x g(x)=sqrt5 x h(x)=2 x+7 Evaluate the function (g ∘ f)(x) for x=2. Write your answer in exact simplified form. Select "Undefined" if applicable. (g ∘ f)(2) is sqrt Undefined

Given the functions:
f(x)=x^3+3 x g(x)=sqrt5 x h(x)=2 x+7

Evaluate the function (g ∘ f)(x) for x=2. Write your answer in exact simplified form. Select "Undefined" if applicable.
(g ∘ f)(2) is sqrt
Undefined

Transcript text: Given the functions: \[ f(x)=x^{3}+3 x \quad g(x)=\sqrt{5 x} \quad h(x)=2 x+7 \] Evaluate the function $(g \circ f)(x)$ for $x=2$. Write your answer in exact simplified form. Select "Undefined" if applicable. $(g \circ f)(2)$ is $\square$ $\sqrt{\square}$ Undefined

Solution

Solution Steps

To evaluate the function $(g \circ f)(x)$ for $x=2$, we need to follow these steps:

Compute $f(2)$ using the function $f(x) = x^3 + 3x$.
Use the result from step 1 as the input for the function $g(x) = \sqrt{5x}$.
Simplify the result to get the final answer.

Step 1: Evaluate $ f(2) $

We start by calculating $ f(2) $ using the function $ f(x) = x^3 + 3x $: \[ f(2) = 2^3 + 3 \cdot 2 = 8 + 6 = 14 \]

Step 2: Evaluate $ g(f(2)) $

Next, we use the result from Step 1 to evaluate $ g(f(2)) $ where $ g(x) = \sqrt{5x} $: \[ g(14) = \sqrt{5 \cdot 14} = \sqrt{70} \] Calculating the numerical value gives: \[ g(14) \approx 8.3666 \]