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Chapter 6: Problem 4

Explain the meaning of the terms 'domain' and 'range' when applied to functions.

Short Answer

Expert verified
Answer: The domain of a function refers to the set of all possible input values (independent variables) for which the function is defined. The range of a function refers to the set of all possible output values (dependent variables) that can be obtained by inputting values from the domain into the function. In other words, the domain is associated with the input values, and the range is associated with the output values that the function can produce.

Step by step solution

01

Domain

The domain of a function is the set of all possible input values (also called independent variables) for which the function is defined. In other words, it is the set of all values that can be plugged into the function to get a valid output or result. For example, if we have a function f(x) = 1/x, the domain would be all real numbers except 0, as dividing by 0 is undefined.
02

Range

The range of a function is the set of all possible output values (also called dependent variables) that can be obtained by inputting values from the domain into the function. In other words, it is the set of all results that can be produced by the function. For example, if we have a function f(x) = x^2, the range would be all non-negative real numbers, as when squaring any real number, the result will always be greater than or equal to 0.
03

Summary

Domain and range are important concepts in understanding how functions behave and what values they can accept and produce. Remember, the domain of a function refers to the set of all possible input values, while the range refers to the set of all possible output values obtained from the input values in the domain.

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Most popular questions from this chapter

Plot a graph of the following functions. In each case state the domain and the range of the function. (a) \(f(x)=3 x+2,-2 \leq x \leq 5\) (b) \(g(x)=x^{2}+4,-2 \leq x \leq 3\) (c) \(p(t)=2 t^{2}+8,-2 \leq t \leq 4\) (d) \(f(t)=6-t^{2}, 1 \leq t \leq 5\)

Given the function \(g(t)=8 t+3\) find (a) \(g(7)\) (b) \(g(2)\) (c) \(g(-0.5)\) (d) \(g(-0.11)\)

Given the function \(f(t)=2 t^{2}+4\) find (a) \(f(x)\) (b) \(f(2 x)\) (c) \(f(-x)\) (d) \(f(4 x+2)\) (e) \(f(3 t+5)(\mathrm{f}) f(\lambda)(\mathrm{g}) f(t-\lambda)\) (h) \(f\left(\frac{t}{\alpha}\right)\)

If \(f(x)=\frac{x-3}{x+1}\) and \(g(x)=\frac{1}{x}\) find \(g(f(x))\).

Explain what is meant by a function.
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