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 StartFraction 4 x plus 7 Over 7 x minus 4 EndFractionf(x)=4x+77x−4;
g left parenthesis x right parenthesis equals StartFraction 7 x Over 7 x minus 4 EndFractiong(x)=7x7x−4(a) Find
(fplus+g)(x).
(fplus+g)(x)equals=StartFraction 11 x plus 7 Over 7 x minus 4 EndFraction11x+77x−4
(Simplify your answer.)What is the domain of fplus+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 nothing EndSetx x≠47x not equals four sevenths.
(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{x x is any real number}.
(b) Find left parenthesis f minus g right parenthesis left parenthesis x right parenthesis(f−g)(x).
left parenthesis f minus g right parenthesis left parenthesis x right parenthesis(f−g)(x)equals=negative StartFraction 3 x minus 7 Over 7 x minus 4 EndFraction−3x−77x−4
(Simplify your answer.)What is the domain of f minus gf−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 nothing EndSetx x≠47x not equals four sevenths.
(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{x x is any real number}.
(c) Find
(ftimes•g)(x).
(ftimes•g)(x)equals=StartFraction 7 x left parenthesis 4 x plus 7 right parenthesis Over left parenthesis 7 x minus 4 right parenthesis squared EndFraction7x(4x+7)(7x−4)2
(Simplify your answer.)What is the domain of ftimes•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 nothing EndSetx x≠47x not equals four sevenths.
(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{x x is any real number}.
(d) Find left parenthesis StartFraction f Over g EndFraction right parenthesis left parenthesis x right parenthesisfg(x).
left parenthesis StartFraction f Over g EndFraction right parenthesis left parenthesis x right parenthesisfg(x)equals=StartFractio n 4 x plus 7 Over 7 x EndFraction4x+77x
(Simplify your answer.)What is the domain of StartFraction f Over g EndFractionfg?
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 EndSetx x≠47x not equals four sevenths.
(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{x x is any real number}.
(e) Find (fplus+g)(33).
(fplus+g)(33)equals=nothing
(Type an integer or a simplified fraction.)
(f) Find (fminus−g)(44).
(fminus−g)(44)equals=nothing
(Type an integer or a simplified fraction.)
(g) Find (ftimes•g)(11).
(ftimes•g)(11)equals=nothing
(Type an integer or a simplified fraction.)
(h) Find left parenthesis StartFraction f Over g EndFraction right parenthesis left parenthesis 2 right parenthesisfg(2).
left parenthesis StartFraction f Over g EndFraction right parenthesis left parenthesis 2 right parenthesisfg(2)equals=nothing
(Type an integer or a simplified fraction.)