If a(x) = 3x + 1 and b(x)= √x-4 , what is the domain of (b*a)(x)

ANSWER:  Domain of a(x) = 3x + 1 and b(x) = x – 4 function is universal set, i.e. (-∞, ∞). SOLUTION: Given, two functions are a(x) = 3x + 1 and b(x) = x – 4,  We need to find what is the domain of (b. a) (x)? We know that, (b. a) (x) is an arithmetic combination of a(x) and b(x) Now, (b. a) (x) = b(x).a(x) = (x – 4).(3x + 1) = x(3x + 1) – 4(3x + 1) [tex]\begin{array}{l}{=3 x^{2}+x-12 x-4} \\ {=3 x^{2}-11 x-4}\end{array}[/tex]Now, let us find the domain of above function. We know that, domain of a function is set of values which are defined under the given function. As the above equation is quadratic equation, no value can give the result as undefined. Hence, domain of given function is universal set, i.e. (-∞, ∞).