In Exercises 7–10, determine from its graph if the function is...

Question

In Exercises 7–10, determine from its graph if the function is one-to-one.

f(x) = 3 - x, x < 0

= 3, x ≥ 0

Accepted Answer

Hello. In this video, we are going to be determining whether the given function is 1 to 1. Now the given function is a piecewise function. That is given to us as g of x is equal to 2 x plus 1. When X is less than 1, and it's equal to the constant function 1, when X is greater than equal to 1. Now, in order for a piecewise function to be 1 to 1, the individual parts of the piece wise have to be 1 to 1 as well. As long as one of these pieces is not 1 to 1, then the entire function will not be 1 to 1. Let's go ahead and start by observing the function when it is defined for all values that are less than one. Now, the function that's defined for the piecewise function when X is less than 1, again, is 2 X + 1. But what's unique about this is that this is a linear function. Linear functions are defined on the entirety of their domain, and what this means is that this part of the function is going to be a 1 to 1 function. Now let's take a look at the part of the function when X is greater than or equal to 1. Now this part of the function is defined as positive one, but more importantly, this is a constant function. Now, the problem with constant functions is that a constant function maps multiple outputs to just one input. So what this means is that constant functions are not 1 to 1, and they're not 1 to 1 because you get multiple outputs for one input. Now the important thing here is that the constant function part of the piece wise is not 1 to 1, and because one itself is not a 1 to 1 function, the solution to this problem is that the entirety of the piecewise function is not 1 to 1. So I hope this video helps you in understanding on how to approach this problem, and we will go ahead and see you all in the next video.

In Exercises 7–10, determine from its graph if the function is one-to-one.f(x) = 3 - x, x < 0 = 3, x ≥ 0

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In Exercises 7–10, determine from its graph if the function is one-to-one.
f(x) = 3 - x, x < 0
= 3, x ≥ 0