find ( f + g ), ( f - g ), ( fg ), and ( \frac{f}{g} ). determine the domain for each function.\n\n( f(x)=5x…

find ( f + g ), ( f - g ), ( fg ), and ( \frac{f}{g} ). determine the domain for each function.\n\n( f(x)=5x - 1 ), ( g(x)=3x^{2} )\n\n( (f + g)(x)=3x^{2}+5x - 1 ) (simplify your answer.)\n\nwhat is the domain of ( f + g )?\n\na. the domain of ( f + g ) is ( {} ). (use a comma to separate answers as needed.)\n\nb. the domain of ( f + g ) is ( (-infty,infty) ). (type your answer in interval notation.)\n\nc. the domain of ( f + g ) is ( varnothing ).\n\n( (f - g)(x)=square ) (simplify your answer.)

find ( f + g ), ( f - g ), ( fg ), and ( \frac{f}{g} ). determine the domain for each function.\n\n( f(x)=5x - 1 ), ( g(x)=3x^{2} )\n\n( (f + g)(x)=3x^{2}+5x - 1 ) (simplify your answer.)\n\nwhat is the domain of ( f + g )?\n\na. the domain of ( f + g ) is ( {} ). (use a comma to separate answers as needed.)\n\nb. the domain of ( f + g ) is ( (-infty,infty) ). (type your answer in interval notation.)\n\nc. the domain of ( f + g ) is ( varnothing ).\n\n( (f - g)(x)=square ) (simplify your answer.)

Answer

Explanation:

Step1: Find ((f - g)(x))

By the definition of ((f - g)(x)=f(x)-g(x)). Given (f(x) = 5x - 1) and (g(x)=3x^{2}), then ((f - g)(x)=(5x - 1)-3x^{2}). Rearrange the terms: ((f - g)(x)=-3x^{2}+5x - 1).

Step2: Determine the domain of (f - g)

The function (y=-3x^{2}+5x - 1) is a polynomial function. For any polynomial function (y = a_{n}x^{n}+a_{n - 1}x^{n-1}+\cdots+a_{1}x + a_{0}) ((n) is a non - negative integer and (a_{i}) are constants), the domain is all real numbers. In interval notation, the domain is ((-\infty,\infty)).

Answer:

((f - g)(x)=-3x^{2}+5x - 1) The domain of (f - g) is ((-\infty,\infty))