Question

For the functions f and g find:

a. (f + g)(x)
b. (f - g)(x)
c. (f • g)(x)
d. (f/g)(x)

f(x) = x - 5, g(x) = 4x + 6

a) 5x - 1, -3, 4x² - 19x - 30, (x - 5)/(4x + 6)
b) -3, 5x - 1, 4x² - 19x - 30, (x - 5)/(4x + 6)
c) 5x - 1, -3, 4x² - 19x + 30, (4x + 6)/(x - 5)
d) 5x - 1, -3, 4x² - 19x + 30, (x - 5)/(4x + 6)

Answer 1

a) (f + g)(x) = 5x - 1, (f - g)(x) = -3, (f • g)(x) = 4x² - 19x - 30, (f/g)(x) = (x - 5)/(4x + 6)

Step-by-step explanation:

To find (f + g)(x), simply add the functions f(x) and g(x):

[ f(x) + g(x) = (x - 5) + (4x + 6) = 5x - 1 ]

For (f - g)(x), subtract g(x) from f(x):

[ f(x) - g(x) = (x - 5) - (4x + 6) = -3 ]

To obtain (f • g)(x), multiply f(x) and g(x):

[ f(x) • g(x) = (x - 5)(4x + 6) = 4x² - 19x - 30 ]

Finally, for (f/g)(x), divide f(x) by g(x):

`\[ (f(x))/(g(x)) = (x - 5)/(4x + 6) \]`

So, the correct option is (a): 5x - 1, -3, 4x² - 19x - 30, (x - 5)/(4x + 6).

In summary, (f + g)(x) is obtained by adding the two functions, (f - g)(x) is found by subtracting, (f • g)(x) is obtained by multiplying, and (f/g)(x) is calculated by dividing the two functions. The given values for a, b, c, and d match the correct results of these operations.