This is kind of a tricky question. First off, the range of a function is not what you're after. You want the codomain. The range of a function is the set of all of the values that are possible as a result of the function acting on every element in the domain. The codomain, in contrast, is more generally thought of as where the function was constrained to fall in the first place, prior to even knowing what the function was.
Think of a game of pool. When you take a shot, the range of where the cue ball will end up (assuming you don't scratch) is on the table. The codomain, however, is the entire three dimensional room. The range constraint of the codomain was due to the function which mapped the ball from its starting point to it's functionally allowed ending point. In this case, the function could be called "Legal Billiard Shot." However, the function could have been, "Throw Cue Ball At Friend's Head" which would have had the same exact codomain, the three dimensional area of the room, but a completely different range.
Now for the actual answer to your question. When composing two functions, say f: x --> y and g: y --> z, which yields g(f(x)) --> z, what you actually need to know is only the codomain of f(x) and only the domain of g(y), and they have to be the exact same set. You can't take a composite function if you can't be guaranteed that the range of the first function, which is a subset of it's codomain, is also a subset of the domain of the second function, ie: every value, y, has to be able to produce an actual, definable result when acted on by g(y).
range
The inverse of the inverse is the original function, so that the product of the two functions is equivalent to the identity function on the appropriate domain. The domain of a function is the range of the inverse function. The range of a function is the domain of the inverse function.
The original function's RANGE becomes the inverse function's domain.
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That all depends on the functions you are given for the problem! When you add or subtract from the original function, then we obtain the new function. If you combine the functions with different domains, then the domain of the addition/subtract obeys whatever domain other function has. For instance: f(x) = 1/x and g(x) = x f(x) + g(x) = (1/x) + x = (1 + x²)/x Then, the domain is all real values except 0 since x = 0 makes the denominator zero, hence making the whole expression undefined. If x = 0, then this makes f(0) undefined.
true
True.
True.
true
true
The domain and range of the composite function depend on both of the functions that make it up.
range
domain
No. If the range of the first function is not the domain of the second function then the composite function is not defined.
Eukaryotes compose the domain Eukaryota.
Eukaryotes compose the domain Eukaryota.
The inverse of the inverse is the original function, so that the product of the two functions is equivalent to the identity function on the appropriate domain. The domain of a function is the range of the inverse function. The range of a function is the domain of the inverse function.