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Chapter 1: Problem 76

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

Short Answer

Expert verified
The function \(g(s)=4s^{2/3}\) is even and its graph is symmetric about the y-axis.

Step by step solution

01

Compute g(-s)

Replace \(s\) with \(-s\) for the function \(g(s)=4s^{2/3}\), resulting in \(g(-s)=4(-s)^{2/3}\). Because the exponent is even, it will eliminate the negative sign, resulting in \(g(-s)=4s^{2/3}\).
02

Compare g(-s) and g(s)

Having computed \(g(-s)\) earlier, and observing that \(g(-s)=g(s)\), this fits the definition of an even function.
03

Determine the symmetry

In the light of this being an even function, the graph is symmetric about the y-axis.

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