Question

f(x) = x + 2 | x + 1 | + 2 | x – 1 | . If f(x) = k has exactly one real solution, then the value of k is

Answer 1

f(k)=k+2+k+1+2+k-1

     4k+4=0   (since k is a factor of f)
     k=-4/4=-1
     ∴k=-1