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Chapter 6: Problem 2

If \(f(x)=8 x+2\) find \(f(f(x))\).

Short Answer

Expert verified
Answer: The composition of the function \(f(x) = 8x + 2\) with itself, \(f(f(x))\), is equal to \(64x + 18\).

Step by step solution

01

Identify the function f(x)

The function is given: \(f(x) = 8x + 2\)
02

Write down f(f(x)) in terms of f(x)

To find \(f(f(x))\), replace \(x\) in the initial function with \(f(x)\). \(f(f(x)) = f(8x + 2)\)
03

Replace f(x) in f(f(x)) with the expression in terms of x

Now, we need to replace the \(f(x)\) in \(f(f(x))\) expression with the initial function expression: \(f(8x + 2) = 8(8x + 2) + 2\)
04

Simplify the expression

Let's simplify the expression to get the final result: \(8(8x + 2) + 2 = 64x + 16 + 2\) \(f(f(x)) = 64x + 18\) So, the composition of the function \(f(x)\) with itself, \(f(f(x))\), is equal to \(64x + 18\).

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