Question

Let f(x) = - 7x³ - 8x² - 6x +1 and g(x) = 5x³ - 6x² - 7x-3.

a) Find (f - 9)(x).

b) Find (f - g)(-1).

Answer 1

To find (f - 9)(x), subtract 9 from the function f(x), resulting in - 7x³ - 8x² - 6x - 8. To find (f - g)(-1), subtract g(x) from f(x) and evaluate at -1, resulting in 13.

Step-by-step explanation:

To find (f - 9)(x), we subtract 9 from the function f(x). Since f(x) = - 7x³ - 8x² - 6x +1, subtracting 9 results in:

(f - 9)(x) = f(x) - 9 = (- 7x³ - 8x² - 6x + 1) - 9 = - 7x³ - 8x² - 6x - 8.

For the second part, to find (f - g)(-1), we need to subtract g(x) from f(x) and then evaluate the result at x = -1:

f(x) = - 7x³ - 8x² - 6x +1

g(x) = 5x³ - 6x² - 7x-3

(f - g)(x) = (- 7x³ - 8x² - 6x +1) - (5x³ - 6x² - 7x-3)

(f - g)(x) = - 7x³ - 8x² - 6x +1 - 5x³ + 6x² + 7x + 3

(f - g)(x) = -12x³ - 2x² + x + 4

Now evaluate at x = -1:

(f - g)(-1) = -12(-1)³ - 2(-1)² + (-1) + 4 = 12 - 2 - 1 + 4 = 13.