Given f(x) = 2 - x2, g(x) = sqrt(x + 2) f(x) = sqrt(x), g(x) = sqrt(1 - x) (a) write formulas for f@g and g@f and find the (b) domain and (c) range of each.

Nann

Nann

Answered question

2020-11-26

Given
f(x)=2x2,g(x)=x+2
f(x)=x,g(x)=1x
(a) write formulas for fg and gf and find the
(b) domain and
(c) range of each.

Answer & Explanation

brawnyN

brawnyN

Skilled2020-11-27Added 91 answers

(a) fg(x)
f(x+2)
2(x+2)2
2(x+2)
x
gf(X)
g(2x2)
2x2+2
4x2
(b) Now, find the domain of the both composite functions.
The domain of the function f(x) consists of all real and the domain of the function g(x) is [2,).
Now check the domain of the composite function fg (x) = -x. The domain of this function consists of all real values.
To find the domain of fg (x), there are some restrictions. But [2,) is a proper subset of the domain of fg (x).
Therefore, the domain of fg (x) will be [2,).
Similarly, check the domain of the composite function gf (x). The domain of this function is [-2, 2].
To find the domain of gf (x), there are some restrictions. But [-2, 2] is a proper subset of the domain of gf (x).
Therefore, the domain of gf (x) will be [-2, 2].
(c) Now, find the range of the both composite functions.
The range of the composite function fg (x) will be all real values.
i.e. Range = (,)
The range of the composite function gf (x) will be 0 to 2.
i.e. Range = [0, 2].

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?