Solveeit Logo
Login

Question

Question: If f(x) = \(\left\{ \begin{array} { l l } 2 + x , & x \geq 0 \\ 2 - x , & x < 0 \end{array} \right....

If f(x) = {2+x,x≥02−x,x<0\left\{ \begin{array} { l l } 2 + x , & x \geq 0 \\ 2 - x , & x < 0 \end{array} \right. , then f(f(x)) is given by

A

f(f(x)) =

B

f(f(x)) =

C

f(f(x)) =

D

f(f(x)) =

Answer

f(f(x)) =

Explanation

Solution

f(f(x)) = {2+f(x),f(x)≥02−f(x),f(x)<0\left\{ \begin{array} { l l } 2 + f ( x ) , & f ( x ) \geq 0 \\ 2 - f ( x ) , & f ( x ) < 0 \end{array} \right.

Since f (x) ≥ 2 ∀ x ∈ R

⇒ f(f(x)) = {4+x,x≥04−x,x<0\left\{ \begin{array} { l l } 4 + x , & x \geq 0 \\ 4 - x , & x < 0 \end{array} \right.