For each pair of functions fand g below, find f (g (x)) and g (f(x)). Then, determine whether f and g are inverses of each other. Simplify your answers as much as possible. (Assume that your expressions are defined for all x in the domain of the composition. You do not have to indicate the domain.) 1 (a) f(x) = x – 2 (b) f(x) , x + 0 3x 1 g (x) = x + 2 8 (x) x + 0 3x f(g (x)) = 0 s(8 (x)) = 0 %3D %3D 8 (F(x)) 8(f(x)) : = 0 Of and g are inverses of each other Of and g are inverses of each other Of and g are not inverses of each other Of and g are not inverses of each other
For each pair of functions fand g below, find f (g (x)) and g (f(x)). Then, determine whether f and g are inverses of each other. Simplify your answers as much as possible. (Assume that your expressions are defined for all x in the domain of the composition. You do not have to indicate the domain.) 1 (a) f(x) = x – 2 (b) f(x) , x + 0 3x 1 g (x) = x + 2 8 (x) x + 0 3x f(g (x)) = 0 s(8 (x)) = 0 %3D %3D 8 (F(x)) 8(f(x)) : = 0 Of and g are inverses of each other Of and g are inverses of each other Of and g are not inverses of each other Of and g are not inverses of each other
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:For each pair of functions fand g below, find f(g (x)) and g (f(x)).
Then, determine whether f and g are inverses of each other.
Simplify your answers as much as possible.
(Assume that your expressions are defined for all x in the domain of the composition.
You do not have to indicate the domain.)
1
(a) f(x) = x – 2
(b) f(x)
x + 0
3x
1
g (x) = x + 2
8 (x)
x + 0
3x
s(8 (x))
f(g (x)) =
8 (f(x)) =
8(f(x)) =
0
Of and g are inverses of each other
Of and g are inverses of each other
Of and g are not inverses of each other
Of and g are not inverses of each other
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