For , consider the function . Which option gives along with its correct…

MATHEMATICS · Single correct · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions

Problem

For a>0, a≠1a>0,\,a\neq1, consider the function F(x)=a2x−1F(x)=a^{2x-1}. Which option gives F−1(x)F^{-1}(x) along with its correct domain? (a) F−1(x)=2log⁡ax+1F^{-1}(x)=2\log_a x + 1, domain (0,∞)(0,\infty) (b) F−1(x)=log⁡ax+12F^{-1}(x)=\dfrac{\log_a x +1}{2}, domain (0,∞)(0,\infty) (c) F−1(x)=log⁡ax+12F^{-1}(x)=\dfrac{\log_a x +1}{2}, domain R\mathbb R (d) F−1(x)=log⁡ax−12F^{-1}(x)=\dfrac{\log_a x -1}{2}, domain (0,∞)(0,\infty)

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