For the given functions: f(x)=sqrt(x-2)g(x)=1-2x find: (a) f o g (b) g o f (c) fo f (d) g o g State the domain of each composite function

sincsenekdq

sincsenekdq

Answered question

2022-09-05

For the given functions:
f ( x ) = x 2 g ( x ) = 1 2 x
find: (a) f o g (b) g o f (c) fo f (d) g o g
State the domain of each composite function

Answer & Explanation

altistkahem

altistkahem

Beginner2022-09-06Added 15 answers

(a) f o g = 1 2 x 2 = 1 2 x
D: x >= -1/2
(b) g o f = 1 2 x 2
D: x >= 2
(c) f o f = ( x 2 ) 2
D: x >= 6
(d) g o g = 1 2 ( 1 2 x ) = 1 2 + 4 x = 1 + 4 x
D: all reals
Slovenujozk

Slovenujozk

Beginner2022-09-07Added 1 answers

a) f o g = 1 2 x 2 = 1 2 x
the domain of this function is :
-1 - 2x >= 0.
-2x >= 1
x<=-1/2 (flip the sign when dividing by negative number)
domain: x<= -1/2
b) g o f = 1 2 x 2 .
Domain: you cannot take a sqrt of a negative number, so x-2>=0,and x>=2.
domain: x >= 2
c) f o f = x 2 2 .
the inside must be nonnegative, so x 2 2 >= 0
x 2 >= 2. However, x - 2 must also be non negative: therefore x>=6.
domain: x >=6
d) g o g: 1 - 2(1 - 2x) = 1 - 2 + 4x = -1 + 4x.
Domain: all real numbers

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