Which one of the following is correct in respect of the function f : R R ⁺ defined as f ( x )=| x +1| ?

Step-by-step solution

Given, f ( x )=| x +1| . Let us check all options. (a) aligned & f ( x )^2= | x ^2+1 | & ( f ( x ))^2=( x +1)^2 & So, f ( x )^2 ( f ( x ))^2 aligned (b) aligned & f (| x |)= | x |+1| & | f ( x )|=| x +1||=| x +1| & f ( x ) | f ( x )| aligned (c) aligned & f ( x + y )=| x + y +1| & f ( x )+ f ( y )=| x +1|+| y +1| & f ( x + y ) f ( x + f ( y )) aligned