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Chapter 2: Q. 80 (page 70)

In Problems 75鈥� 82, find the difference quotient of f; that is, find f(x+h)-f(x)h,h鈮�0,for each function. Be sure to simplify.

f(x)=1x+3

Short Answer

Expert verified

The value off(x+h)-f(x)h=1(x+3)(x+h+3)

Step by step solution

01

Step 1. Given Information

In this problems we have to find the difference quotient of f; that is, find f(x+h)-f(x)h,h鈮�0,for given function. Be sure to simplify.

The given function is
f(x)=1x+3

02

Step 2. Firstly we find the value of f(x+h)We find the value of f(x+h) by putting x=x+h in given function.

f(x+h)=1x+h+3

03

Step 3. Putting the value of f(x) and f(x+h) in the f(x+h)- f(x)h

f(x+h)-f(x)h=1x+h+3-1x+3hf(x+h)-f(x)h=1h1x+h+3-1x+3

The LCD of x+h+3anda+3is(x+3)(x+h+3)so multiply with the LCD.

role="math" localid="1646239803210" f(x+h)-f(x)h=1h1x+h+3路(x+3)(x+h+3)(x+3)(x+h+3)-1x+3路(x+3)(x+h+3)(x+3)(x+h+3)f(x+h)-f(x)h=1hx+3(x+3)(x+h+3)-x+h+3(x+3)(x+h+3)f(x+h)-f(x)h=1hx+3-x+h+3(x+3)(x+h+3)f(x+h)-f(x)h=1hx+3-x-h-3(x+3)(x+h+3)f(x+h)-f(x)h=1h路h(x+3)(x+h+3)f(x+h)-f(x)h=1(x+3)(x+h+3)

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