Uploaded by TheIntegralCALC on 23.06.2011

Transcript:

Hi, everyone! Welcome back to integralcalc.com. Today we’re going to be doing another problem

with domain and range. And in this one, we’ve been asked to find the domain of the function

f(x) = 10^2x + log(21 – 3x). And what we need to remember about domain is that the

domain of a function is all of the numbers for which the function is defined. The easiest

way to figure out domain is by first finding where the function is not defined, if anywhere.

And then just exclude those values from your domain. So you need to look for the give-aways.

In this case, we’ve kind of got two terms here. We have 10^2x and we have log (21 – 3x)

and we can treat those separately. There’s nothing really restrictive about

10^2x. There’s no number that you could plug in for x, if you’re just looking at

10^2x, that would make this part of this function undefined. So there aren’t really any values

there that we have to consider not being in the domain. But it’s a different story with

the log function here because as you may or may not know, you can not take log of zero

or of a negative number. What that means is that 21 – 3x must be greater than zero.

Everything inside the log function must be greater than zero because again, log of zero

is undefined and log of a negative number is undefined. We can solve this inequality

by adding 3x to both sides and we get 21 > 3x. If we divide both sides by 3, we’ll get

that 7 must be greater than x or in other words, that x has to be less than 7. So in

order for this function to be defined, x has to be less than 7 which means that the domain

we can just write as x must be less than 7. Not < 7 but < 7. If the domain were 7 itself,

we would get zero inside the log function and that’s undefined. Remember that domain

is all values of x where the function is defined and in this case, that is all values less

than 7. So the domain is that x has to be less than 7. Anyway, that’s it. I hope that

video helped you guys and I will see you in the next one. Bye!

with domain and range. And in this one, we’ve been asked to find the domain of the function

f(x) = 10^2x + log(21 – 3x). And what we need to remember about domain is that the

domain of a function is all of the numbers for which the function is defined. The easiest

way to figure out domain is by first finding where the function is not defined, if anywhere.

And then just exclude those values from your domain. So you need to look for the give-aways.

In this case, we’ve kind of got two terms here. We have 10^2x and we have log (21 – 3x)

and we can treat those separately. There’s nothing really restrictive about

10^2x. There’s no number that you could plug in for x, if you’re just looking at

10^2x, that would make this part of this function undefined. So there aren’t really any values

there that we have to consider not being in the domain. But it’s a different story with

the log function here because as you may or may not know, you can not take log of zero

or of a negative number. What that means is that 21 – 3x must be greater than zero.

Everything inside the log function must be greater than zero because again, log of zero

is undefined and log of a negative number is undefined. We can solve this inequality

by adding 3x to both sides and we get 21 > 3x. If we divide both sides by 3, we’ll get

that 7 must be greater than x or in other words, that x has to be less than 7. So in

order for this function to be defined, x has to be less than 7 which means that the domain

we can just write as x must be less than 7. Not < 7 but < 7. If the domain were 7 itself,

we would get zero inside the log function and that’s undefined. Remember that domain

is all values of x where the function is defined and in this case, that is all values less

than 7. So the domain is that x has to be less than 7. Anyway, that’s it. I hope that

video helped you guys and I will see you in the next one. Bye!