The functions f and gare defined as f(x-5x-3and g(x):-8x2. a)Find the domain off

Question

The functions f and gare defined as f(x-5x-3and g(x):-8x2. a)Find the domain off,g,f+g,f-g.fgtt, and b) Find t+gkx), t-)) a)The domain of f is Type your answer in interval notation) The domain of g is Type your answer in interval notation.) The domain of f + g is (Type your answer in interval notation.) The domain off-gD (Type your answer in interval notation.) The domain of fg is Type your answer in interval notation) The domain of f is (Type your answer in interval notation.) The domain of) is Type your answer in interval notation.) The domain of(1)(x) is Type your answer in interval notation ) b)d+ g)l) (Siemplity your answer d-gXX)=(Smplify your answer ) (5g)(x)- (Simplify your answer ) emio)-(Singlity your answer ) nter your answer in each of the answer boxes Type here to search

Explanation / Answer

f(x) = 5x - 3

g(x) = -8x^2

a) domain of f = (-infinity , + infinity )

domain of g = (-infinity , + infinity )

domian of f+g = (-infinity , + infinity )

domain of f - g = (-infinity , + infinity )  

domain of fg = (-infinity , + infinity )

domian of f/g = ( - infinity , 0 ) U (0 , infinity )

domain of g/f = ( -infinity , 3/5 ) U ( 3/5 , infinity )

b) ( f+g)(x) = f(x) + g(x)

= -8x^2 + 5x -3

c) ( f- g)(x) = f(x) - g(x)

= 5x - 3 + 8x^2

= 8x^2 + 5x -3

d) (fg)(x) = f(x) g(x)

= ( 5x -3 ) ( -8x^2 )

= -40x^3 + 24x^2

e) (ff)(x) = f(x) f(x)

( 5x - 3 ) (5x - 3)

= 25x^2 - 30x + 9

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