Question

We can say that composition of functions is commutative since fog (x) = gof (x).

• A. True
• B. False

Answer 1

The correct option is B

False

Composition of functions is not commutative.

Let g: A -> B and f : C -> D be the two functions

Then fog : A -> D if and only if B is a subset of C. Then the value of function fog for x will be f(g(x)).

In, fog(x) the function g takes values of x in domain of it, the output of g will be the input for f and resultant will be f(g(x))

Also gof : C -> B if and only if D is the subset of A. Then the value of function gof for x will be g(f(x))

In, gof(x) the function f takes values of x in domain of it, the output of f will be the input for g and resultant will be g(f(x)).

Since g is not equal to f, g(f(x)) need not be equal to f(g(x))