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Chapter 2: Problem 36

Evaluate each function at the given values of the independent variable and simplify. \(f(x)=\frac{4 x^{3}+1}{x^{3}}\) a. \(f(2)\) b. \(f(-2)\) c. \(f(-x)\)

Short Answer

Expert verified
a. \(f(2) = 4.125\),\nb. \(f(-2) = 3.875\),\nc. \(f(-x) = -f(x)\)

Step by step solution

01

Evaluation of the function at \(x=2\)

Substitute \(x=2\) into the function: \(f(2) =\frac{4 (2)^{3}+1}{(2)^{3}} = \frac{32+1}{8} = 4.125\)
02

Evaluation of the function at \(x=-2\)

Substitute \(x=-2\) into the function: \(f(-2) =\frac{4 (-2)^{3}+1}{(-2)^{3}} = \frac{-32+1}{-8} = 3.875\)
03

Evaluation of the function at \(x=-x\)

Substitute \(x=-x\) into the function: \(f(-x) =\frac{4 (-x)^{3}+1}{(-x)^{3}} = \frac{- 4x^{3}+1}{-x^{3}} = -f(x)\. So, \(f(-x)\) equals to the negative of the original function \(f(x)\).

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