Math  /  Algebra

QuestionFind the domain, range, inverse domain, and inverse range of the function f(x)=2x6f(x)=2x-6.

Studdy Solution
The range of the inverse function is the set of all possible output values (usually y-values), which result from the inverse function. For the given inverse function f1(x)=x+62f^{-1}(x) = \frac{x+6}{2}, there are no restrictions on the output values. Therefore, the range is also all real numbers.
Rangeoff1(x)=(,)Range\, of\, f^{-1}(x) = (-\infty, \infty)So, the domain and range of the function f(x)=2x6f(x)=2x-6 and its inverse f1(x)=x+62f^{-1}(x) = \frac{x+6}{2} are all real numbers.

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