Question

Let fn +1(x) = fn(x) + 1, if n is a multiple of
3 = f(x) – 1 otherwise.
If fi(1) = 0, then what is f50(1) ?
(2011)
(a) - 18
(b) – 16
(c) – 17
(d) Cannot be determined
​

Answer 1

Answer:

ANSWER

f:W→W

f(x) ={n−1,n=oddn+1,n=even}

When n is odd

f(x

1

)=f(x

2

)

n

1

−1=n

2

−1

n

1

=n

2

When n is even

f(x

1

)=f(x

2

)

n

1

+1=n

2

+1

n

1

=n

2

So, f(x) is one-one

When n is odd

f(x)=n−1

y=n−1

n=y+1

Put n in f(x)

f(x)=y+1−1

f(x)=y

When n is even

f(x)=n+1

y=n+1

n=y−1

Put n in f(x)

f(x)=y−1+1

f(x)=y

So, f(x) is onto

So, the function f(x) is bijective. Hence is invertible.

f(x)=n−1 if n is odd

y=n−1

n=y−1

f

−1

(x)=y−1 if n is odd

f(x)=n+1 if n is even

y=n+1

n=y+1

f

−1

(x)=y+1 if n is even