Find f(x+h) given the function...

Question

If f(x)=x+3, what is ((f(x+h)-f(x)/h))??

 

Please show the steps taken in order to get the answer.

The following choices are provided for answers:

A.) f

B.) (h+6/h)

C.) 0

D.) 1

Answer 1

The answer is choice (D) or 1. To arrive at the answer first you need to note how the expression is written.

Then way it is presented you  ((f(x+h)-f(x)/h))  could be written as [ x+3+h - (x+3)/h]. Upon simplifying you obtain

(xh+3h+h^2 -x+3)/h, which is not one of the choices. If you write [ ( f(x+h) -f(x) )/h ] then upon substituting f(x) = x+3 you obtain:

 

(x+3+h - (x+3)) / h : Here f(x+h) is x+h +3  and you divide the entire numerator expression f(x+h) -f(x) by h

 

simplify the above and you are left with h/h which reduces to 1.

 

The example you provided is a simple limit  expression of the form  [f(a+h) -f(a)] / h

 

additional note:an excellent overview of  the notation and concept of a limit can be found here toward teh end of the page: http://tutorial.math.lamar.edu/Classes/CalcI/Tangents_Rates.aspx

Answer 2

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

 

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

 

Hence, the answer is ____.