Functions again!

[Shelveen]

Let me try to explain where I am having trouble...
what im thinking is that I have to take the g(2) and basically plug it into the X for (x-2)/(x+3), but that gives me (0/5), which doesn't work. Can someone explain how this is suppose to work please? I have watched a ton of youtube videos on it, and its not helping.

 

[ksdhart2]

what im thinking is that I have to take the g(2) and basically plug it into the X for (x-2)/(x+3)...

Yes, that's correct. That's how you evaluate g(2).

...but that gives me (0/5), which doesn't work....

What's wrong with that? Surely you recognize that \(\frac{0}{5} = 0\) because \(\frac{0}{\text{(something)}}\) is always 0 unless that "something" is also 0. But that's not the case here, so what's the problem?

 

[Dr.Peterson]

There's nothing wrong with 0/5; zero divided by any non-zero number is zero.

So now just plug 0 into f, and you'll have it. You're doing much better than you thought.

But if it were true that you got stuck with something that doesn't exist (such as 5/0), you'd just say that your input was not in the domain of the composite function -- that would not be a problem, just a fact about the function!

 

[Shelveen]

Nice! Thank you guys! So I did f(0)=0^2 + 0 -6 = -6. Perfect!

 

[Steven G]

That is correct. 0 is not a bad number (just ask the people who just paid off a big loan!)

 

[HallsofIvy]

I suspect the OP was confusing this with dividing by 0,