Question

NO LINKS!! URGENT HELP PLEASE!!

If a and h are real numbers, find the following values for the given function.
f(x) = 3 -2x

a. f(-a)=
b. -f(a)=
c. f(a + h)
d. f(a) + f(h)
e. (f(a + h) - f(a))/h if h ≠ 0

Answer 1

Explanation:

a. f(-a) = 3 - 2(-a) = 3 + 2a

b. -f(a) = -(3 - 2a) = -3 + 2a

c. f(a + h) = 3 - 2(a + h) = 3 - 2a - 2h

d. f(a) + f(h) = (3 - 2a) + (3 - 2h) = 6 - 2a - 2h

e. (f(a + h) - f(a))/h = [3 - 2(a + h) - (3 - 2a)]/h = [-2h]/h = -2, if h ≠ 0.

Answer 2

a. To find f(-a), substitute -a for x in the given function:

f(-a) = 3 - 2(-a) = 3 + 2a

Therefore, f(-a) = 3 + 2a.

b. To find -f(a), evaluate f(a) and then multiply by -1:

f(a) = 3 - 2a

-f(a) = -(3 - 2a) = -3 + 2a

Therefore, -f(a) = -3 + 2a.

c. To find f(a + h), substitute a + h for x in the given function:

f(a + h) = 3 - 2(a + h) = 3 - 2a - 2h

Therefore, f(a + h) = 3 - 2a - 2h.

d. To find f(a) + f(h), evaluate f(a) and f(h), and then add them:

f(a) = 3 - 2a

f(h) = 3 - 2h

f(a) + f(h) = (3 - 2a) + (3 - 2h) = 6 - 2a - 2h

Therefore, f(a) + f(h) = 6 - 2a - 2h.

e. To find (f(a + h) - f(a))/h if h ≠ 0, substitute the expressions for f(a + h) and f(a) into the formula:

(f(a + h) - f(a))/h = ((3 - 2a - 2h) - (3 - 2a))/h = (-2h)/h = -2

Therefore, (f(a + h) - f(a))/h = -2 if h ≠ 0.