Let f:R→Rbe a function defined by f(x+1)=f(x)−5f(x)−3∀x∈R. Then which of the following statement(s) is/are true ?

f(x+1)=f(x)−5f(x)−3                (1)or      f(x)f(x+1)−3f(x+1)=f(x)−5or     f(x)=3f(x+1)−5f(x+1)−1Replacing x by (x - 1), we getf(x−1)=3f(x)−5f(x)−1              (2)Using(1), f(x+2)=f(x+1)−5f(x+1)−3=f(x)−5f(x)−3−5f(x)−5f(x)−3−3=2f(x)−5f(x)−2                             (3)Using (2), f(x−2)=3f(x−1)−5f(x−1)−1=33f(x)−5f(x)−1−53f(x)−5f(x)−1−1                        =2f(x)−5f(x)−2                          (4)Using (3) and (4), we have f (x + 2) = f (x - 2).Therefore f(x+4)=f(x), i.e., f(x) is periodic with period 4.