Let f, g :R--- R be 2 functions defined as f(x) = |x| + x and g(x) = |x|-x for - Maths - Relations and Functions

Question

Let f, g :R--->R be 2 functions defined as f(x)
= |x| + x and g(x) = |x|-x for everyx E
R Then find fog and gof

Geetika Sharma · Accepted Answer

Dear student,

Following is the answer to your query,

f(x)=|x| + x  ∀ x∈ℝg(x) = |x| – x  ∀ x∈ℝf∘g=f(g(x))=||x| – x| + |x| – x⇒f∘g=0∀ x≥0-4x∀ x<0Similarly:g∘f=g(f(x))=||x| + x| –(|x| + x)⇒g∘f=0∀ x≥00∀ x<0

Let f, g :R--->R be 2 functions defined as f(x) = |x| + x and g(x) = |x|-x for everyx E R. Then find fog and gof.