Math Problem Statement
For the given functions f and g, complete parts (a)-(h). For parts (a)-(d), also find the domain. f left parenthesis x right parenthesis equals StartRoot 5 x EndRoot; g left parenthesis x right parenthesis equals 7 x minus 4 Question content area bottom Part 1 (a) Find (fplusg)(x). (fplusg)(x)equals StartRoot 5 x EndRoot plus 7 x minus 4 (Simplify your answer. Type an exact answer, using radicals as needed.) Part 2 What is the domain of fplusg? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The domain is StartSet x vertical line x greater than or equals 0 EndSet . (Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) Your answer is correct.B. The domain is StartSet x vertical line x is any real number EndSet. Part 3 (b) Find left parenthesis f minus g right parenthesis left parenthesis x right parenthesis. left parenthesis f minus g right parenthesis left parenthesis x right parenthesisequals StartRoot 5 x EndRoot minus 7 x plus 4 (Simplify your answer. Type an exact answer, using radicals as needed.) Part 4 What is the domain of f minus g? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The domain is StartSet x vertical line x greater than or equals 0 EndSet . (Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) Your answer is correct.B. The domain is StartSet x vertical line x is any real number EndSet. Part 5 (c) Find (ftimesg)(x). (ftimesg)(x)equals StartRoot 5 x EndRoot left parenthesis 7 x minus 4 right parenthesis (Simplify your answer. Type an exact answer, using radicals as needed.) Part 6 What is the domain of ftimesg? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The domain is StartSet x vertical line x greater than or equals 0 EndSet . (Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) Your answer is correct.B. The domain is StartSet x vertical line x is any real number EndSet. Part 7 (d) Find left parenthesis StartFraction f Over g EndFraction right parenthesis left parenthesis x right parenthesis . left parenthesis StartFraction f Over g EndFraction right parenthesis left parenthesis x right parenthesis equals StartFraction StartRoot 5 x EndRoot Over 7 x minus 4 EndFraction (Simplify your answer. Type an exact answer, using radicals as needed.) Part 8 What is the domain of StartFraction f Over g EndFraction ? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The domain is StartSet x vertical line nothing EndSet . (Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. The domain is StartSet x vertical line x is any real number EndSet.
Solution
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Math Problem Analysis
Mathematical Concepts
Function Operations
Radicals
Linear Functions
Domain Restrictions
Formulas
(f + g)(x) = f(x) + g(x)
(f - g)(x) = f(x) - g(x)
(f × g)(x) = f(x) × g(x)
(f/g)(x) = f(x) / g(x)
Theorems
Square Root Function Domain Restriction
Denominator Zero Restriction
Suitable Grade Level
Grades 10-12
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