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.
