Question 984605: find the domain and range of:
f(x)=
i)1-|x|
ii)x^2 -1 /x-1
iii)-|x|
iv)|x-1|
v)|x-2|/2-x
vi)root of(3-2x) Answer by ikleyn(52797) (Show Source):
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1) f(x) = 1-|x|. The domain is the set of all real numbers. The range is the set of all real numbers <= 1.
2) f(x) = . The domain is the set of all real numbers =/= 0. The range is the set of all real numbers.
Figure. Plot of the function
3) f(x) = -|x|. The domain is the set of all real numbers. The range is the set of all non-positive real numbers.
4) f(x) = |x-1|. The domain is the set of all real numbers. The range is the set of all non-negative real numbers.
5) f(x) = . The domain is the set of all real numbers =/= 2. The range is {-1, 1}, i.e. the set consisting of two numbers -1 and 1 only.
(Actually, this function is equal to 1 at x < 2 and equal to -1 at x > 2).
6) f(x) = . The domain is the set of all real numbers x <= . The range is the set of all non-negative real numbers.
