Mathematics

Problem

Two real-valued functions are defined as

f(x)=|x-4|

and

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

, where

x\neq 1

. a. Compute

f(0)

g(0)

f(5)

and

g(5)

. b. For the inputs

x=0

and

x=5

, determine for which input(s) the equality

f(x)=g(x)

holds. Show your calculations clearly. c. Examine whether

f\bigl(g(2)\bigr)

is defined. If it is, find its value; if not, state the reason.