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Chapter 2: Q. 7 (page 68)

If the domain of fis all real numbers in the interval [0,7]and the domain of g is all real numbers in the interval [-2,5], the domain of f+gis all real numbers in the interval _________.

Short Answer

Expert verified

If the domain of fis all real numbers in the interval[0,7]and the domain of g is all real numbers in the interval[-2,5], the domain off+gis all real numbers in the interval [0,5]

Step by step solution

01

Step 1. Given information 

If the domain of fis all real numbers in the interval [0,7]and the domain of g is all real numbers in the interval [-2,5], the domain off+g is all real numbers in the interval _________.

02

Step 2. Main Idea:

Domainoff+g=Domainoff鈭�Domainofg

03

Step 3. It is given that:

Domain of f=[0,7]

Domain of g=[-1,5]

Therefore,

f+g=[0,7]鈭�[-1,5]f+g=[0,5]

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Most popular questions from this chapter

Use the given graph of the function f to answer parts (a) 鈥� (n).

(a) Find f0 and f6.

(b) Find f2and f-2.

(c) Is f3positive or negative?

(d) Is f-1positive or negative?

(e) For what values of x is fx=0?

(f) For what values of x is localid="1650172833683" fx<0?

(g) What is the domain of f ?

(h) What is the range of f ?

(i) What are the x-intercepts?

(j) What is the y-intercept?

(k) How often does the line y = -1 intersect the graph?

(l) How often does the line x = 1 intersect the graph?

(m) For what value of x does fx=3?

(n) For what value of x does fx=-2?

A wire 10meters long is to be cut into two pieces. One piece will be shaped as an equilateral triangle, and the other piece will be shaped as a circle.

Part (a): Express the total area Aenclosed by the pieces of wire as a function of the length x of a side of the equilateral triangle.

Part (b): What is the domain of A?

Part (c): Graph A=Ax. For what value of xis Asmallest?

Medicine Concentration: The concentration C of a medication in the bloodstream t hours after being administered is modeled by the function C(t)=-0.002t4+0.039t3-0.285t2+0.766t+0.085.

(a) After how many hours will the concentration be highest?

(b) A woman nursing a child must wait until the concentration is below 0.5 before she can feed him. After taking the medication, how long must she wait before feeding her child?

In Problems 39-68, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, y=x2) 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.

h(x)=int(-x)

Match each graph to its function.

A. Constant function B. Identity function C. Square function D. Cube function E. Square root function F. Reciprocal function G. Absolute value function H. Cube root function

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