Let f and g be two functions from R into R, defined by f(x) = |x| + x and g(x) = |x| - x for all x ∈ R. Find f o g and g o f.
To Find: Inverse of f o g and g o f.
Given: f(x) = |x| + x and g(x) = |x| - x for all x ∈ R
f o g (x) = f(g(x)) = |g(x)| + g(x) = ||x| - x | + |x| - x
Case 1) when x
0
f(g(x)) = 0 (i.e. |x| - x)
Case 2) when x
0
f(g(x)) = -4x
g o f (x) = g(f(x)) = |f(x)| - f(x) = ||x| + x | - |x| - x
Case 1) when x
0
g(f(x)) = 0 (i.e. |x| - x)
Case 2) when x
0
g(f(x)) = 0
1