domain and range of f(g(x))?

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]

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.

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 ]

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

yes