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Chapter 1: Problem 75

Determine whether the function is even, odd, or neither. Then describe the symmetry. $$f(s)=4 s^{3 / 2}$$

Short Answer

Expert verified
The function \(f(s) = 4s^{3 / 2}\) is an odd function and exhibits symmetry with respect to the origin.

Step by step solution

01

Checked Symmetry - Step 1

First, replace \(s\) with \(-s\) in the original function i.e. \(f(-s) = 4*(-s)^{3 / 2}\) and simplify the equation.
02

Checked Symmetry - Step 2

Upon simplifying it, we obtain \(f(-s) = 4*\sqrt[2]{(-s)^3}\) which can be rewritten as \(f(-s) = 4*(-s^{3 / 2})\). Thus, it's equivalent to \(-f(s)\). Therefore, the function is odd.
03

Identify Symmetry - Step 3

Since the function is odd, it exhibits symmetry with respect to the origin.

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Most popular questions from this chapter

The work \(W\) done when lifting an object varies jointly with the object's mass \(m\) and the height \(h\) that the object is lifted. The work done when a 120 -kilogram object is lifted 1.8 meters is 2116.8 joules. How much work is done when lifting a 100 -kilogram object 1.5 meters?

The cost per unit in the production of an MP3 player is 60 dollars. The manufacturer charges 90 dollars per unit for orders of 100 or less. To encourage large orders, the manufacturer reduces the charge by 0.15 dollars per MP3 player for each unit ordered in excess of 100 (for example, there would be a charge of 87 dollars per MP3 player for an order size of 120 ). (a) The table shows the profits \(P\) (in dollars) for various numbers of units ordered, \(x .\) Use the table to estimate the maximum profit. $$\begin{array}{|l|c|c|c|c|c|}\hline \text { Units, } x & 130 & 140 & 150 & 160 & 170 \\\\\hline \text { Profit, } P & 3315 & 3360 & 3375 & 3360 & 3315 \\\\\hline\end{array}$$ (b) Plot the points \((x, P)\) from the table in part (a). Does the relation defined by the ordered pairs represent \(P\) as a function of \(x ?\) (c) Given that \(P\) is a function of \(x,\) write the function and determine its domain. (Note: \(P=R-C\) where \(R\) is revenue and \(C\) is cost.)

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Given $$f(x)=x^{2}$$ is \(f\) the independent variable? Why or why not?

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