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For question 30, state the domain and range of the function. ​

For question 30, state the domain and range of the function. ​-example-1
User OCcSking
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Explanation:

normally a simple expression in x has no natural limitations.

but for fractions we have to pay attention, because we have to avoid results like .../0, as they are undefined.

so, 4x + 1 has no limitations, but x² - 1 must never be 0.

the only "bad cases" are

x² - 1 = 0

x² = 1

x = ±1

therefore, the domain (the definition of the valid values for x) is

x € R, x <> -1 and x <> 1

the range (the definition of valid values for y) is then any value between -infinity and +infinity.

simply because around x=-1 and x=+1 the tendency goes against - and + infinity.

User Andymcgregor
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