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

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Solution

$f (1) = 1^{2} = 1 f (2) = 2^{2} = 4 f (3) = 3^{2} = 9 f (4) = 4^{2} = 16 f (5) = 5^{2} = 25$
Hence, the range of the function is { $1, 4, 9, 16, 25$ }
Since the elements in co-domain does not equal to the elemets in range $\Rightarrow f$ is not onto.
Image is not same for two domain elements in $f$ , hence it is one-one.

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

f(1)=12=1f(2)=22=4f(3)=32=9f(4)=42=16f(5)=52=25Hence, the range of the function is {1,4,9,16,25}Since the elements in co-domain does not equal to the elemets in range ⇒f is not onto.Image is not same for two domain elements in f, hence it is one-one.

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