Problem

Given the functions: \[ f(x)=x^{3}-5 x \quad g(x)=\sqrt{3 x} \quad h(x)=3 x-4 \] Evaluate the function $(f \circ f)(x)$ for $x=2$. Write your answer in exact simplified form. Select "Undefined" if applicable. $(f \circ f)(2)$ is Undefined

Solution

Step 1 :Given the function \(f(x)=x^{3}-5x\), we need to evaluate the function \(f \circ f(x)\) at \(x=2\). This means we need to evaluate the function \(f(x)\) at the point \(f(2)\). In other words, we need to find the value of \(f(f(2))\).

Step 2 :First, we find the value of \(f(2)\). Substituting \(x=2\) into the function \(f(x)\), we get \(f(2)=2^{3}-5(2)=-2\).

Step 3 :Next, we substitute this value into the function \(f(x)\) to find \(f(f(2))\). So, \(f(f(2))=f(-2)=(-2)^{3}-5(-2)=2\).

Step 4 :Final Answer: The value of \(f \circ f(2)\) is \(\boxed{2}\).

From Solvely APP
Source: https://solvelyapp.com/problems/8141/

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