Question

Given f(x)=5x-5 and g(x)=3x², first find f+g,f-g,fg, and (f)/(g). Then determine the domain for each function.

Answer 1

To find f+g, we add the two functions together to get 3x² + 5x - 5. To find f-g, we subtract the second function from the first to get -3x² + 5x - 5. To find fg, we multiply the two functions together to get 15x³ - 15x². To find f/g, we divide the first function by the second to get (5/3) * (1/x - 1). The domain for each function is the set of all real numbers.

Step-by-step explanation:

To find f+g, we add the two functions together:

(f+g)(x) = f(x) + g(x) = (5x-5) + (3x²)

(f+g)(x) = 3x² + 5x - 5

To find f-g, we subtract the second function from the first:

(f-g)(x) = f(x) - g(x) = (5x-5) - (3x²)

(f-g)(x) = -3x² + 5x - 5

To find fg, we multiply the two functions together:

(fg)(x) = f(x) * g(x) = (5x-5) * (3x²)

(fg)(x) = 15x³ - 15x²

To find f/g, we divide the first function by the second:

(f/g)(x) = f(x) / g(x) = (5x-5) / (3x²)

(f/g)(x) = (5/3) * (1/x - 1)

The domain for each function is the set of all real numbers.