Question

Using the function, f(x) = 2-x , find the following

a) f(x+h)
b) f(x+h)-f(x)
c)f(x+h)-f(x)/h

Answer 1

To find f(x+h), substitute (x+h) into f(x). To find f(x+h)-f(x), substitute (x+h) and x into f(x) and subtract. To find (f(x+h)-f(x))/h, divide the expression by h.

Step-by-step explanation:

To find a) f(x+h), we substitute (x+h) into the function f(x). So, f(x+h) = 2-(x+h).

b) To find f(x+h)-f(x), we substitute (x+h) and x into the function f(x) and subtract. So, f(x+h)-f(x) = [2-(x+h)] - [2-x].

c) To find (f(x+h)-f(x))/h, we divide the expression from part b) by h. So, (f(x+h)-f(x))/h = [2-(x+h)] - [2-x] / h.

Answer 2

Let's evaluate each expression using the given function \( f(x) = 2 - x \):

a) \( f(x + h) \)

\[ f(x + h) = 2 - (x + h) = 2 - x - h \]

b) \( f(x + h) - f(x) \)

\[ f(x + h) - f(x) = (2 - x - h) - (2 - x) = -h \]

c) \( \frac{f(x + h) - f(x)}{h} \)

\[ \frac{f(x + h) - f(x)}{h} = \frac{-h}{h} = -1 \]

So, for the given function \( f(x) = 2 - x \):

a) \( f(x + h) = 2 - x - h \)

b) \( f(x + h) - f(x) = -h \)

c) \( \frac{f(x + h) - f(x)}{h} = -1 \)