Q. 11

# Let f and g be tw

Answer :

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

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