Question

Let A = {1, 2, 3, 4, 5}, B = N and f: A → B be defined by f(x) = x². Find the range of f. Identify the type of function.

Answer 1

Now, A = {1, 2, 3, 4, 5};

B = {1, 2, 3, 4, … }

Given f: A → B and f(x) = x²

f(1) = 1² = 1;

f(2) = 4;

f(3) = 9;

f(4) = 16;

f(5) = 25.

Range of f = {1, 4, 9, 16, 25}

Since distinct elements are mapped into distinct images, it is a one-one function.

However, the function is not onto, since 3 ∈ B but there is no x ∈ A such that

f(x) = x² = 3.