For the pair of function f and g, determine the domain of f/g.
F(x) = 
,g(x) = 4-x
Solution:-
The domain of t/g is the set of all values common to the domains of t and g, excluding values for which g(x) is 0.
The domain of a function defined by an equation is the set of all number for which real values of the function can be calculated. A function can be undefined at a number because calculating its value results in an undefined in an undefined operation like division by zero or an even root of a negative number.
For the function , f(x) =. The denominator is zero for x= 3, which result in an undefined value. Therefore, the domain of f is {x I x is a real number and x
3}.
For the function , g(x) = 4 – x, a value can be calculated for any real number x. Therefore, the domain of g is {x I x is a real number}.
The domain of the quotient also excludes all values for which f(x) is zero. Therefore solve the equation
4 – x = 0.
X = 4
The domain of f/g is the set of all values common to { x I x is a real number and x 3} and {x I x is a real number}, and also excluding x = 4.
Therefore , the domain of f/g is {x I x is a real number and x 3 and x 4}.