Answer the following questions with respect to the pair of functions and .

MATHEMATICS · Multi-part · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions

Problem

Answer the following questions with respect to the pair of functions y=2xy=2^{x} and y=log⁡2xy=\log_{2}x. (i) Verify that the two functions are inverses of each other by evaluating their compositions both ways. (ii) Hence write the domain and the range of each function. (iii) Using your result from part (ii), determine the domain and range of the functions: (a) y=log⁡2(3−x)y=\log_{2}(3-x) (b) y=2x−5y=2^{x-5}

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