For the given functions f and g, complete parts (a)-(h). For parts (a)-(d), also find the domain. f(x) = 4x + 7/7x - 4: g(x) = 7x/7x - 4 (a) Find (f + g)(x). (f + g)(x) = (Simplify your answer.) What is the domain of f + g? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The domain is {x| }. (Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed) B. The domain is {x| x is any real number}. (b) Find (f - g)(x) (f - g)(x) = (Simplify your answer.) What is the domain of f - g? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The domain is {x| }. (Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. The domain is {x| x is any real number}. (c) Find (f - g)(x). (f middot g)(x) = (Simplify your answer.) What is the domain of f middot g? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The domain is {x| }. (Use integers or fractions for any numbers in the expression Use a comma to separate answers as needed.) B. The domain is {x| x is any real number}. (d) Find (f/g)(x). (f/g)(x) = (Simplify your answer.) What is the domain of f/g? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The domain is {x| }. (Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. The domain is {x| x is any real number}. (e) Find (f + g)(5). (f + g)(5) = (Type an integer or a simplified fraction.) (f) Find (f - g)(2). (f - g)(2) = (Type an integer or a simplified fraction.) (g) Find(f middot g)(1). (f middot g)(1) = (Type an integer or a simplified fraction.) (h) Find (f/g)(4). (f/g)(4) = (Type an integer or a simplified fraction.)
f(x) = ( 4x + 7 ) / ( 7x - 4 )
g(x) = 7x / ( 7x - 4 )
a) (f+g)(x) = f(x) + g(x)
= ( 4x + 7 ) / ( 7x - 4 ) + 7x / ( 7x - 4 )
= ( 11x + 7 ) / ( 7x - 4 )
domain is { x | x not equal to 4/7 }
b) (f-g)(x) = f(x) - g(x)
( 4x + 7 ) / ( 7x - 4 ) - 7x / ( 7x - 4 )
( - 3x + 7 ) / ( 7x - 4 )
domain is { x | x not equal to 4/7 }
c) (f * g)(x) = f(x) * g(x)
= ( 4x + 7 ) / ( 7x - 4 ) * 7x / ( 7x - 4 )
= ( 28x^2 + 49x ) / (7x-4)^2
domain is { x | x not equal to 4/7 }
d) (f/g)(x) = f(x) / g(x)
= ( 4x + 7 ) / ( 7x - 4 ) / 7x / ( 7x - 4 )
= (4x + 7 ) / 7x
domain is { x | x not equal to 0 }
e) (f+g)(5) = ( 11(5) + 7 ) / ( 7(5) - 4 )
= 62 / 31
f) (f-g )(2) = ( - 3(2) + 7 ) / ( 7(2) - 4 )
= 1 / 10
g) (f*g)(1) = ( 28(1)^2 + 49(1) ) / (7(1)-4)^2
= 77 / 9
h) ( f/g)(4) = (4(4) + 7 ) / 7(4)
= 23/28
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