i want to know the domain and range of this function 1/x^2+5/2 .
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Domain:  Possible x values

There's nothing like a fraction bar or square root or anything that mean certain values of x can't be used.

The domain is all real numbers.

 

Range:  Possible f(x) values

There's an x^2.  Those are always positive.

As x becomes very small (close to 0), 1/(x^2) becomes very large, blowing up to + infinity.

As x becomes very large (either + infinity or - infinity), 1/(x^2) approaches 0, but never becomes negative.  The limit as x goes to infinity (+ or -) of 1/(x^2) is 0.  The smallest f(x) can be is 5/2.

The range is 5/2 to infinity.
by Level 13 User (103k points)

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