Mathematics

Problem

(i) State the definition of the composite function

g\circ f

. (ii) Explain, with reasoning, how the domain of

g\circ f

is related to the domains of

f

and

g

. (iii) Let

f(x)=x^{2}-4x+3

and

g(t)=\dfrac{1}{t-1}

. Determine the domain of

g\circ f

, giving clear justification for every restriction you impose.