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(a) Do even continuous functions have an inverse? (b) Odd functions?

(a) No(b) only if they are one-to-one

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 1

Inverse Functions

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Lectures

01:29

Let $f(x)$ be a function. …

00:28

Is the inverse of a one-to…

01:12

Even and Odd Functions

01:48

The function $\mathrm{f}(\…

02:24

(a) Prove that the functio…

03:08

If $2 f(x)+3 f\left(\frac{…

00:44

Does a constant function h…

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Are the statements true or…

So if we're given an even continuous function, this will just by definition not ever be 1 to 1. Because remember, first, something to be even This implies that if we have, like f of A, this is equal to f of negative A. But we have where a is not equal to negative eight. And so this is just by definition of something being even and well, that would further imply that it is not 1 to 1. So there is no even function that is continuous and, um is 1 to 1. Now, for odd and continuous, we actually have a couple of cases because one example of a function that does have it in verse would be something like X cute. So this is an odd function, and if we look at the graph, it looks like this. But there's another function where this does not follow. Um, that is odd. Being sine of x and sine of X is odd function, and it looks like this essentially, so that is not 1 to 1. So we can have this. Um, but we need that it be 1 to 1, so yes, but needs to be 1 to 1. So let me just go ahead and box are answers for these

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