To evaluate f ( x ) = 1 x + 1 at a number, substitute the number for x in the definition of f ( x ) The given function of the values f ( a ) = 1 a + 1 , f ( a + h ) = 1 a + h + 1 , f ( a + h ) − f ( a ) h = − 1 ( a + h + 1 ) ( a + 1 ) Given information: consider the function f ( x ) = 1 x + 1 Calculation: Start by assume x is the variable of a function f ( x ) . Evaluate the values of the function f ( x ) = 1 x + 1 for the given values of the variable x Plug the value x = a , in the function f ( x ) = 1 x + 1 then the value of f ( a ) . f ( a ) = 1 a + 1 Plug the value x = a + h , in the function f ( x ) = 1 x + 1 thenthe value of f ( a + h ) . f ( a + h ) = 1 a + h + 1 f ( a + h ) − f ( a ) h = 1 a + h + 1 − 1 a + 1 h Since f ( a + h ) = 1 a + h + 1 , f ( a ) = 1 a + 1 = 1 h ( ( a + 1 ) − ( a + h + 1 ) ( a + h + 1 ) ( a + 1 ) ) = − 1 ( a + h + 1 ) ( a + 1 ) Thus, f ( a ) = 1 a + 1 , f ( a + h ) = 1 a + h + 1 , f ( a + h ) − f ( a ) h = − 1 ( a + h + 1 ) ( a + 1 )

BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 2.1, Problem 38E
Solution

To evaluate f(x)=1x+1 at a number, substitute the number for x in the definition of f(x)

The given function of the values

  f(a)=1a+1,f(a+h)=1a+h+1,f(a+h)f(a)h=1(a+h+1)(a+1)

Given information:consider the function f(x)=1x+1

Calculation:

Start by assume x is the variable of a function f(x) .

Evaluate the values of the function f(x)=1x+1 for the given values of the variable x

Plug the value x=a, in the function f(x)=1x+1 then the value of f(a).

  f(a)=1a+1

Plug the value x=a+h, in the function f(x)=1x+1 thenthe value of f(a+h).

  f(a+h)=1a+h+1

  f(a+h)f(a)h=1a+h+11a+1h        Since f(a+h)=1a+h+1,f(a)=1a+1=1h((a+1)(a+h+1)(a+h+1)(a+1))=1(a+h+1)(a+1)

Thus, f(a)=1a+1,f(a+h)=1a+h+1,f(a+h)f(a)h=1(a+h+1)(a+1)

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