Question 395426: f(x) = x^2 - 3 and g(x) = 4x + 5
What is (f + g)(3)? I get 23.
What is the domain of (f + g)(3)? Is is 3 or 23?
Thanks
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! What is (f + g)(3)? I get 23.
You are correct. Good job.
What is the domain of (f + g)(x)? Is is 3 or 23? Both and more (see why below)
Note: I'm assuming you meant (f + g)(x) and NOT (f + g)(3)
Remember what the domain is: the domain is the set of all possible inputs. Since 3 and 23 work for inputs, they are clearly part of the domain. But are these the only values of x that work? The answer is no. There are definitely a lot more. For example, inputs like x=0, x=5, and x=21 all work too.
It turns out that ANY real number works as an input for (f+g)(x). So this means that the domain is the set of all real numbers.
If you need more help, email me at jim_thompson5910@hotmail.com
Also, feel free to check out my tutoring website
Jim
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