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Chapter 2: Q. 75 (page 70)

In Problems 75鈥� 82, find the difference quotient of f; that is, find localid="1646236938641" f(x+h)-f(x)h,h鈮�0,for each function. Be sure to simplify.

f(x)=4x+3

Short Answer

Expert verified

The value off(x+h)-f(x)h=4

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 islocalid="1646237247753" f(x)=4x+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)=4(x+h)+3f(x+h)=4x+4h+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=4x+4h+3-(4x+3)hf(x+h)-f(x)h=4x+4h+3-4x-3hf(x+h)-f(x)h=4hhf(x+h)-f(x)h=4

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Most popular questions from this chapter

If f(x)=-3xifx<-10ifx=-12x2+1ifx>-1

Find: (a)f(-2) and (b) f(-1) (c)f(0)

If x=-2, the value of the expression 3x2-5x+1xis _______.

Graph the function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. Verify your results using a graphing utility.

f(x)=x2+4

Suppose that the x-intercepts of the graph of y=f(x)are-5and 3.

(a) What are the x-intercepts of the graph of y=f(x+2)?

(b) What are the x-intercepts of the graph of y=f(x-2)?

(c) What are thex-intercepts of the graph of y=4f(x)?

(d) What are thex-intercepts of the graph of y=f(-x)?

True or False Every relation is a function.
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