Which of the following statements is ALWAYS true for two functions and whenever the…

MATHEMATICS · Single correct · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Which of the following statements is ALWAYS true for two functions

f

and

g

whenever the compositions are defined? (a)

(g\circ f)(x)=(f\circ g)(x)

for every

x

(b)

(g\circ f)(x)

exists only when

g

is invertible (c) In general,

(g\circ f)(x)\neq(f\circ g)(x)

(d)

(g\circ f)(x)

exists only when f and g have the same domain