Inverse domain

Geometry Level pending

Given that g ( x ) = tan ⁡ ( x − 3 π / 2 ) + 6 g(x)= \tan (x-3π/2)+6 . What is the domain of g − 1 ( x ) g^{-1}(x) ?

( − 3 π / 2 , 3 π / 2 ) (-3π/2, 3π/2) ( − 3 π / 2 , 0 ) (-3π/2, 0) ( 5 , 7 ) (5, 7) ( − ∞ , ∞ ) (-\infty,\infty)

Ryan S by Ryan S , 20, USA

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1 solution

Alex Li
Jun 23, 2015

Because the tangent function has a range of all real numbers, and adding a constant does not change that, the inverse must have a domain of all real numbers.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Yeah, the constant doesn't impact it, so the domain is all real numbers.

Ryan S - 5 years, 11 months ago

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