Question

In: Advanced Math

For the given functions f and​ g, complete parts​ (a)-(h). For parts​ (a)-(d), also find the...

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 7 x plus 9 Over 9 x minus 7 EndFractionf(x)=7x+99x−7​;

g left parenthesis x right parenthesis equals StartFraction 9 x Over 9 x minus 7 EndFractiong(x)=9x9x−7​(a) Find

​(fplus+​g)(x).

​(fplus+​g)(x)equals=nothing

​(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 .

​(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=nothing

​(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 .

​(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=nothing

​(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 .

​(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=nothing

​(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 .

​(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)(44​).

​(fplus+​g)(44​)equals=nothing

​(Type an integer or a simplified​ fraction.)​(f) Find

​(fminus−​g)(33​).

​(fminus−​g)(33​)equals=nothing

​(Type an integer or a simplified​ fraction.)​(g) Find

​(ftimes•​g)(22​).

​(ftimes•​g)(22​)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.)

Solutions

Expert Solution

Colby Messinger answered 2 years ago
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