Explanation Domain: The domain of the function is defined as the set of complete possible values which will make the function work and give the output as real values. Range: The range of the function is the set of all possible resulting values that we get by substituting the values of domain. Given: A function as f ( x ) = x 2 – x + 5 Formula Used: 1. For domain of a square root function, set the expression inside the square root greater than or equal to zero. 2. Range of the quadratic function is a parabola (either upward or downward opening). If it is upward parabola, the function will not take any values below the vertex and if it is downward parabola, it will not take any values above the vertex. 3. Discriminant of quadratic equation a x 2 + b x + c is given as b 2 – 4 a c Calculation: Given function is f ( x ) = x 2 – x + 5 Domain of the function f ( x ) = x 2 – x + 5 : To find the domain, the expression inside the square root should be greater than or equal to zero. x 2 – x + 5 ≥ 0 Discriminant of the above quadratic equation is: ( − 1 ) 2 – 4 ( 1 ) ( 5 ) = − 19 Discriminant of the quadratic equation comes to be negative; hence the quadratic equation will be either positive or negative for all the values of x . Checking the value of expression at x = 0 , we get ( 0 ) 2 – 0 + 5 = 5 Since value is positive, thus the domain of the given function is the set of all real numbers. Thus, the domain of the function f ( x ) = x 2 – x + 5 is all real numbers In Interval notation form, domain is ( ∞ , ∞ ) Range of the function f ( x ) = x 2 – x + 5 : The expression is a quadratic equation

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

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Chapter 1, Problem 16CRE

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The domain and the range of the function f(x) = x2– x + 5

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Chapter 1 Solutions

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The domain and the range of the function f ( x ) = x 2 – x + 5

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