Question

Find the indicated function values.

f(x) =2x-3/x-4
a. f (0)
b. f(3)
c. f(-4)
d. f(-5)
e. f(a+h)
f. Why must 4 be excluded from the domain of

Answer 1

To find the indicated function values of f(x) = (2x - 3) / (x - 4), we substitute the given values of x into the function. We exclude 4 from the domain of the function because it results in division by zero.

Step-by-step explanation:

To find the indicated function values, we substitute the given values of x into the function f(x) = (2x - 3) / (x - 4). Let's evaluate each part:

1. a. To find f(0), we substitute 0 for x: f(0) = (2*0 - 3) / (0 - 4) = (-3) / (-4) = 3/4 = 0.75.
2. b. To find f(3), we substitute 3 for x: f(3) = (2*3 - 3) / (3 - 4) = (6 - 3) / (-1) = 3 / -1 = -3.
3. c. To find f(-4), we substitute -4 for x: f(-4) = (2*(-4) - 3) / (-4 - 4) = (-8 - 3) / (-8) = -11/8 = -1.375.
4. d. To find f(-5), we substitute -5 for x: f(-5) = (2*(-5) - 3) / (-5 - 4) = (-10 - 3) / (-9) = -13/(-9) = 13/9 = 1.444.
5. e. To find f(a+h), we substitute (a+h) for x: f(a+h) = (2(a+h) - 3) / (a+h - 4).

4 must be excluded from the domain of f(x) because it results in a division by zero. When x = 4, the denominator of the function becomes zero and division by zero is undefined.