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Nonsense/Without solution = Report

Find the Domain and Range​

NonsenseWithout Solution ReportFind The Domain And Range class=

Sagot :

Answer:

DOMAIN AND RANGE

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  • Find the domain by finding where the function is defined and the range is the set of values that correspond with the domain.

[tex]1. \: f(x) = \sqrt{x - 2} [/tex]

[tex]\tt\Large\green{Domain}[/tex]: [tex]\tt\Large\blue{(2,∞),{(x|x≥2)}}[/tex]

[tex]\tt\Large\green{Range}[/tex]: [tex]\tt\Large\blue{(0,∞)l,{(y|y≥0)}}[/tex]

[tex]2. \: f(x) = x {}^{2} [/tex]

[tex]\tt\Large\green{Domain}[/tex]: [tex]\tt\Large\blue{(−∞,∞),{(x|x∈R)}}[/tex]

[tex]\tt\Large\green{Range}[/tex]: [tex]\tt\Large\blue{(0,∞),{(y|y≥0)}}[/tex]

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- K -

MissyArelleeeeeidn

•Answers:

[tex]\large \bold{\tt Practice \: Exercise \: 2:}[/tex]

[tex] \tt Domain \: and \: Range:[/tex]

[tex] \tt4. \: f(x) = \sqrt{x - 2} \\ \tt \: Domain:[2,\infty\} ,\{x|x≥2\}\\ \tt{Range:( - \infty, \infty)},\{y|y \in R\}[/tex]

[tex] \tt5. \: f(x) = x {}^{2} \\ \tt \: Domain:( - \infty, \infty),\{y|y \in R\}\\ \tt{Range:[0,\infty\} ,\{x|x≥0\}}[/tex]

• Explanation:

Domain is the set of all the values of x while range is the set of all the values of y that satisfy the given equation.

For Number 4,

Domain:

[tex] \tt if \: x \: is \: equal \: to \: 2 \\ y = \sqrt{x - 2} \\ y = \sqrt{2 - 2} \\ y = \sqrt{0 } \\ y = 0 \\ = = = = = = = = = = = \\ \tt if \: x \: is \: greater \: than \: 2 \\ y = \sqrt{x - 2} \\ y = \sqrt{6 - 2} \\ y = \sqrt{4} \\ y = ±2 \\ = = = = = = = = = = = = \\ \tt if \: x \: is \: less \: than \: 2 \\ y = \sqrt{1 - 2} \\ y = \sqrt{ - 1} \\ y = {i} [/tex]

Therefore, the domain can be 2 and any number that is greater than 2 but can't be less than 2.

Range:

[tex] \tt if \: y \: is \: equal \: to \: 0 \\ 0 = \sqrt{x - 2} \\ x = 2 \\ = = = = = = = = = = = \\ \tt if \: y\: is \: greater \: than \: 0 \\ 2 = \sqrt{x - 2} \\ x = 6 \\ = = = = = = = = = = = = \\ \tt if \: y\: is \: less \: than \: 0 \\ - 1 = \sqrt{x - 2} \\ x = 3[/tex]

Therefore, the range can be 0 and any number that is greater than 0 even the numbers less than 0.

✓You can do the same with number 5 to check whether the answer is correct.

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