How would I find the domain and range of a function f(g(x)) if I have the domain of both f(x) and g(x)? For a simple example, if I have f(x) = x + 2 where x>10 and g(x) = 2x - 1 where x≤20, what would I do to find the domain and range of f(g(x)) without actually graphing them out? Thanks!
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Well looking at g(x), the domain is (-∞,20] and f(x), the domain is (10,∞). Put them together, the domain of their composition will be (10,20] (10 is not included but 20 is)
To find the range, first we have to perform the composition
f(g(x)) means f(2x-1)=(2x-1)+2=2x+1
when x=10, f(g(10))=21
when x=20, f(g(20))=41
the range will be (21,41]
Demiurge42
The domain of f∘g is always the domain of g as long as the composition is possible. For it to be possible, the range of g must be a subset of the domain of f.
Domain of f(x) = (10, ∞)
Domain of g(x)= (-∞, 20]
Range of g(x) = (-∞, 39]
The range of g is not a subset of the domain of f so you can't take the composition of f with g.
ted s
for domain of " f(g(x)) " you need 2 things : 10 < 2x - 1 and x ≤ 20---> x in ( 11/2 , 20 ]
f(g(x)) = 2x - 1 + 2 = 2x + 1....thus range is (12, 41 ]
xyzzy
in this case.... the domain and range of f(x) and g(x) are both the real numbers.
so the domain and range of f(g(x)) is also the real numbers.
if g = x^2 with the same f(x)
then the range of g = real numbers >= 0... and f(g(x)) would have the domain of real numbers and range of real numbers >=2
of if f(x) = sqrt (x) then the domain of f(x) is real numbers >= 0
so the domain of f(g(x)) is real numbers such that 2x - 1 >= 0
2x>= 1
x>= 1/2
real numbers >= 1/2
Anonymous
yes