If f(x) = 1- (1/x), then f(-n) is equal to...?

Question

If f(x) = 1- (1/x), then f(-n) is equal to...?

a) f(n)

b) 1/(f(n))

c) f(-1/n)

d) 1/(f(n+1))

d) is the correct answer, but how do you get it as the answer?

Answer 1

It is easy to work backwards, but who would ever think to do so in answering this question!

f(n+1) = 1 - 1/(n+1) = (n+1-1)/(n+1) = n/(n+1)

1/f(n+1) = (n+1)/n = 1 + 1/n = f(-n)