Question

f(x +h)-f(x)For the function defined as follows, find (a) f(x + h), (b) f(x + h) – f(x), and (c)f(x)= 4/x

Answer 1

Given the function:

`f(x)=(4)/(x)`

We will find the following:

a) f(x+h)

So, we will substitute with x = x+h

`f(x+h)=(4)/(x+h)`

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

`\begin{gathered} f(x+h)-f(x)=(4)/(x+h)-(4)/(x) \\ \\ f(x+h)-f(x)=(4x-4(x+h))/(x(x+h)) \\ \\ f(x+h)-f(x)=(4x-4x-4h)/(x(x+h)) \\ \\ f(x+h)-f(x)=(-4h)/(x(x+h)) \end{gathered}`

c) [f(x+h) - f(x)]/h

`\begin{gathered} (f(x+h)-f(x))/(h)=(-4h)/(x(x+h)\cdot h) \\ \\ (f(x+h)-f(x))/(h)=(-4)/(x(x+h)) \end{gathered}`