Question

Find (f-g)(x) when f(x) = 2x² + 6/3x and g(x) = sqrt(x) - 8/3x.

a. -x² - (sqrt(x) + 2)
b. x² - (sqrt(x) + 2)
c. -x² + (sqrt(x) - 2)
d. x² + (sqrt(x) - 2)

Answer 1

To find (f-g)(x), subtract the function g(x) from the function f(x). Simplify the resulting expression by combining like terms.

Step-by-step explanation:

To find (f-g)(x), we need to subtract the function g(x) from the function f(x). Let's start with the given functions:

f(x) = 2x² + (6/3)x

g(x) = √x - (8/(3x))

Now, we substitute these functions into (f-g)(x) and simplify:

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

(f-g)(x) = (2x² + (6/3)x) - (√x - (8/(3x)))

(f-g)(x) = 2x² + (6/3)x - √x + (8/(3x))

Therefore, the answer is x² + (7/3)x - √x + (8/(3x)).