Hello!
I really need help with these domain questions ASAP. I've added the answer I thought it's supposed to be but apparently i'm wrong!
Hi,Remember that the domain of the two functions has to satisfy (be a subset of) the domains of the individual functions. For example take the f-g question
f(x) = \(\displaystyle \sqrt{5-x},\, x\, \epsilon\, (-\infty,\, 5]\)
g(x) = \(\displaystyle \sqrt{x^2-4},\, x\, \epsilon\, (-\infty,\, 2]\, or\, x\, \epsilon\, [2, \, \infty)\)
Now we take the two segment of g(x) separately. For the left hand segment, x must be less than or equal to 2. That will satisfy f(x), so we can use the complete left hand segment for f-g. For the right hand segment, x must be greater than or equal to 2 but f(x) says we must also be less than or equal to 5. So, to satisfy both, the right hand segment must be from 2 to 5 inclusive and we have
h(x) = f(x) - g(x), \(\displaystyle x\, \epsilon\, (-\infty,\, 2]\, or\, x\, \epsilon\, [2, 5]\)