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 x0


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 x0


g(f(x)) = 0 (i.e. |x| - x)


Case 2) when x 0


g(f(x)) = 0


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

Fill in theMathematics - Exemplar

Let f : [2, ∞) <sMathematics - Exemplar

Let f : N Mathematics - Exemplar

Fill in theMathematics - Exemplar

Let f :R →<Mathematics - Exemplar

Let f : [0, 1] <sMathematics - Exemplar

Which of the follMathematics - Exemplar