(a) domain ...
(why?)
range ...
is between what two values?
(b) domain ...
for all , so what is the domain?
range ...
Hi, just wonderin if I could have some help with these two questions: each of them asks to find the domain and the range using calculus techniques, and as I am reveiwing this after doing this 12 weeks ago, I am a bit hazy as to what's required.
(a)f(x)=cos sqrt(e^x-1)
(b) g(x)=1//(x^2+1)
if anyone could help and explain fully, that would be greatly appreciated
Basically finding the domain means that all the places in where the function is defined. So for example
1) Find the domain of . The domain is All real numbers except 1. Because and u cannot divide by 0.
So for ur first example
1) . cos(x) is defined for all real numbers, but is real only for (because is not a real number, its a complex number).
As for the range, range is basically all the values ur function can take if u plug in x's from ur domain only.
For example
2) Find the Range of . Since we said the domain of f was all real numbers except 1. We see that pluggin in , for makes the denominator in makes the denominator < 1, which means the function it it self can become as large as So for our range is . Now take So our range can take on values from So our range for x > 1 is plus which means range is Now since we did x > 1, now we try x < 1, so for x < 1, we see that for if our denominator takes on the values in the interval . and if x < 0, we get a small negative denominator, and the function takes on every value from [-1, 0). So our range is , which means that our whole range is , basically ur function can take on every value except 0.