Equal Function in Maths – Definition and Examples

Here you will learn what is equal function in maths with definitions and examples.

Let’s begin –

Equal Function in Maths

Definition : Two functions f and g are said to be equal iff

(i) domain of f = domain of g

(ii) co-domain of f = codomain of g.

and (iii) f(x)  = g(x) for every x belonging to their common domain.

If two functions f and g are equal, then we write f = g.

Also Read : Types of Functions in Maths – Domain and Range

Example : Let A = {1, 2}, B = {3, 6} and f : A \(\rightarrow\) B given by f(x) = \(x^2\) + 2 and g : A \(\rightarrow\) B given by g(x) = 3x. Then, we observe that f and g have the same domain co-domain.

Also we have, f(1) = 3 = g(1) and f(2) = 6 = g(2)

Hence,  f = g.

Example : Let f : R – {2} \(\rightarrow\) R be defined by f(x) = \(x^2 – 4\over x – 2\) and g : R \(\rightarrow\) R be defined by g(x) = x + 2. Find whether f = g or not.

Solution :  Clearly, f(x) = g(x) for all x \(\in\) R – {2}.

But f(x) and g(x) have different domains.

Infact, domain of f = R – {2} and domain of g = R. Therefore, f \(\ne\) g.

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