Question

The function f:N>R is defined by f(n) =2^n.The range of the function is
A. The set of all even positive integers
B. N
C. R
D. A subset of set of all even positive integers

Answer 1

answer : option (D) A subset of set of all even positive integers.

explanation : The function $f:\mathbb{N}\rightarrow\math{R}$ is defined by f(n) = 2ⁿ.

domain of function is set of all natural numbers. e.g., Domain = {1, 2, 3, 4, 5, ....}

so, f(1) = 2¹ = 2

f(2) = 2² = 4

f(3) = 2³ = 8

f(4) = 2⁴ = 16

....... .....

hence, range of function is set A= {2, 4, 8, 16, ...... }

set of all even positive integers is B = {2, 4, 6, 8, 10, 12, 14, 16 , .......}

hence it is clearly shown that , set A is subset of set B.

so, range of the given function is subset of all even positive integers.

Answer 2

Answer:

Step-by-step explanation:

The function f:N>R is defined by f(n) =2^n.The range of the function is

A. The set of all even positive integers

B. N

C. R

D. A subset of set of all even positive integers

Option D is correct

A subset of set of all even positive integers

2ⁿ =  even  (for n>0 )

but not every even number like 6 ≠ 2ⁿ

so A subset of set of all even positive integers