Question

The function f: N-R is defined by f ( n )= 2^n . The range of the function is ( 1 ) the set of all even positive integers (2) N (3) R ( 4 ) a subset of set of all even positive integers ​

Answer 1

The subsets of X − x 0 with odd cardinality become subsets with even cardinality if element is added to each of them. This gives us 2 n − 2 + 2 n − 2 = 2 n − 1 subsets of with even cardinality. So in both cases the answer is 2 n − 1 . There is ( n 2 k ) different sets of size for 1 ≤ k ≤ n / 2 .

Answer 2

Answer:

Range of the given function f(n) : (0 , ∞)

Step-by-step explanation:

The function f : N → R is defined by :

$f(n)=2^n$

The range of this function will be same as an exponential function.

The value of the exponential function cannot be negative.

The largest value of the function is positive infinity

Thus the range of the function f(n) is : y > 0

⇒ Range : f(n) > 0

Interval notation : (0 , ∞)