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What is the domain and range of #y=sec^2x+1#?

Answer 1

Ethan Adkins

#"Domain="RR-{(2k+1)pi/2 | k in ZZ}.#

#"Range="{ x in RR | x >=2}, or, [2,oo).#

Recall that the Domain of #sec# fun. is #RR-{(2k+1)pi/2 | k in ZZ}#.

Obviously, the Domain of the specified fun is also.

#because, |secx| >= 1 :. sec^2x >=1, &, :., y=sec^2x+1 >=2.#

This indicates that the fun's range is,

#{ x in RR | x >=2}, or, [2,oo).#

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Answer 2

Nathan Axel

Domain: All real numbers except where cos(x) = 0. Range: All real numbers greater than or equal to 1.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.