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Chapter 5: Q. 101 (page 271)

Is every odd function one-to-one? Explain.

Short Answer

Expert verified

No, every odd function is not one-to-one because if a function is odd then $f (- x) = - f (x)$ and one-to-one implies that $f (a) = f (b) .$

Step by step solution

01

Step 1. Given Information

We have to explain that is every odd function one-to-one.

02

Step 2. Explanation

Let the function $f (x) = \tan x$ , it is an odd function but it is not one-to-one. Therefore, every odd function is not one-to-one and we can find out by looking at the following graph, by doing a horizontal line test, we get that the line intersects at many points. Thus, it signifies that the function is not one-to-one.

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Most popular questions from this chapter

Solve the equation $3^{- x} = 81$

and verify your results using a graphing utility.

In Problems 61–72, the function f is one-to-one. Find its inverse and check your answer.

$f (x) = \frac{3 x}{x + 2}$

Evaluate each expression using the graphs of $y = f (x)$ and $y = g (x)$ shown in the figure.

(a) $(g \circ f) (- 1)$ (b) $(g \circ f) (0)$ (c) $(f \circ g) (- 1)$ (d) $(f \circ g) (4)$ .

If $5^{- x} = 3$ , what does $5^{3 x}$ equal?

The graph of an exponential function is given. Match each graph to one of the following functions.

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