Consider the following function f(x)=2x/3x^2-3 what is the domain of the function and what is the range of the function

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22-01-2019
Mathematics

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Consider the following function f(x)=2x/3x^2-3 what is the domain of the function and what is the range of the function

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lisboa lisboa · Answer 1 · 2019-01-22T02:25:56+01:00

Answer:

domain (-infinity, -1) U(-1,1) U (1, infinity)

range is (-infinity, infinity)

Step-by-step explanation:

Domain is the set of all x values that makes the function defined

We need to look at x values that makes the function undefined

When denominator =0 then function is undefined

we look at the x values that makes the denominator 0. Set the denominator =0 and solve for x

3x^2 - 3=0

3x^2 = 3

divide by 3 on both sides

x^2 = 1

take square root on both sides

x= +-1 , so x=+1 and x=-1

x=-1 and +1 makes the denominator 0. so we ignore -1 and +1 in the domain

Domain is set of all numbers except -1 and +1

(-infinity, -1) U(-1,1) U (1, infinity)

Range is the set of y values

for every value of x we get an y value

we have only 2x in the numerator . so there is no restriction for y values

So y is all real numbers

range is (-infinity, infinity)

shubheetutor shubheetutor · Answer 2 · 2021-10-23T15:27:12+02:00

Domain: [tex](-\infty , -1) U(-1,1) U (1, \infty )[/tex]

Range: [tex](-\infty ,\infty )[/tex]

Domain is defined as the values of [tex]x[/tex] for which the function is defined.

So, we have to find the values of [tex]x[/tex] for which the function is not defined that is the denominator is [tex]0[/tex].

So, we have to find those values of [tex]x[/tex] for which denominator is [tex]0[/tex].

[tex]3x^2-3=0\\ \\ \Rightarrow x^2=\frac{3}{3}=1[/tex]

Take square root on both sides,

[tex]x=\pm 1[/tex] So, [tex]x=-1[/tex] and [tex]x=1[/tex]

Hence, at [tex]x=-1[/tex] and [tex]x=1[/tex] the denominator 0. So, we ignore [tex]-1[/tex] and [tex]1[/tex] in the domain.

[tex]\therefore[/tex] Domain is set of all numbers except [tex]-1[/tex] and [tex]1[/tex].

Domain: [tex](-\infty , -1) U(-1,1) U (1, \infty )[/tex]

Range is defined as set of elements of [tex]y[/tex] . So, for every value of [tex]x[/tex] we get a value of [tex]y[/tex].

We have [tex]2x[/tex] in the numerator. So, there is no restriction for values of [tex]y[/tex].

Therefore, [tex]y[/tex] is all real numbers.

Hence, Range: [tex](-\infty ,\infty )[/tex]

Learn more about domain and range.

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