Paragraph: Let f(x)=[|x|-|x-1|]^2 Question: Which of the following equations is/are correct? 1. f (-2)= f (5) 2. f ^ (-2)+ f ^ (0.5)+ f ^ (3)=4 Select the correct answer using the code given below:

Step-by-step solution

Given f(x)=(|x|-|x+1|)^2f(x)= array cc 1 & x 0 (2 x-1)^2 & 0 x 1 1 & x 1 array . For x=-2 aligned & f(x)=1 so f(-2)=1 & For x=5 & f(x)=1 f(5)=1 aligned Hence f(-2)=f(5) Now, for x=-1 aligned & f^ (x)=0 & f^ (-2)=0 aligned For x=0.5f^ (x)=8 f^ (0.5)=8 For x=3 aligned & f^ (x)=0 f^ (3)=0 & f^ (-2)+f^ (0.5)+f^ (3)=8 4 aligned Only statement 1 is correct.