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Chapter 5: Q. 122 (page 287)

The hyperbolic sine function, designated by sinhx, is defined as:

sinhx=12ex-e-x

Part (a): Show that fx=sinhxis an odd function.

Part (b): Graph fx=sinhxusing a graphing utility.

Short Answer

Expert verified

Part (a): To prove fx=sinhxis an odd function, substitute localid="1646236259756" f-xin the equation and solve the equation.

Part (b): The graph of the functionfx=sinhx is given below,

Step by step solution

01

Part (a) Step 1. Given information.

Consider the given question,

sinhx=12ex-e-x

Assume fx=sinhx.

Then we can say,

f-x=12e-x-e--x=12e-x-ex=-12ex-e-x=-fx

Hence,fxis an odd function.

02

Part (b) Step 1. Graph the function.

Consider the given function,

fx=sinhx

Plot the function,

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