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Chapter 2: Q.39 (page 90)

Determine algebraically whether each function is even, odd, or neither.

fx=x+x

Short Answer

Expert verified

fxis neither even nor odd function.

Step by step solution

01

Given information.

The function,fx=x+x.

02

Write definition of even function and odd function.

  • A function fxis said to be an even function if f-x=fx.
  • A function fxis said to be an odd function iff-x=-fx.
03

Calculate f-x.

Replace xby -xinto the function fx=x+x.

f-x=-x+-x=-x+x

Clearly, f-x鈮�fxandf-x鈮�-fx

So, by definition:fxis neither even nor odd function.

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Most popular questions from this chapter

Suppose that the graph of a function f is known. Then the graph of y=f(x-2)may be obtained by a(n) ________ shift of the graph of f to the ________ a distance of2 units.

Suppose that the x-intercepts of the graph of y=f(x)are-5and 3.

(a) What are the x-intercepts of the graph of y=f(x+2)?

(b) What are the x-intercepts of the graph of y=f(x-2)?

(c) What are thex-intercepts of the graph of y=4f(x)?

(d) What are thex-intercepts of the graph of y=f(-x)?

Match each graph to its function.

A. Constant function

B. Identity function

C. Square function

D. Cube function

E. Square root function

F. Reciprocal function

G. Absolute value function

H. Cube root function

If 4,2is a point on the graph of y=f(x), which of the following points must be on the graph of y=f2(x)?

The slope of the line containing the points (-2, 3) and (3, 8) is ________.
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