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What is the inverse function of #f(x) = 4/(x + 2)# and what is the domain and range?

Answer 1

Benjamin Achtenberg

Refer to explanation

We have that

#y=4/(x+2)=>x+2=4/y=>x=4/y-2#

hence #y^-1=4/x-2#

the domain is #R-{0}# and the range is #R-{2}#

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Answer 2

Christian Antunez

The inverse function of ( f(x) = \frac{4}{x + 2} ) is ( f^{-1}(x) = \frac{4}{x} - 2 ). The domain of ( f(x) ) is all real numbers except -2, and the range of ( f(x) ) is all real numbers except 0. The domain of ( f^{-1}(x) ) is all real numbers except 0, and the range of ( f^{-1}(x) ) is all real numbers except -2.

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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.