Mathematics, 29.07.2019 07:00 Izzyfizzy
Given the function f(x) = 0.5(3)x, what is the value of f−1(7)? this question has been asked before but the answer is unclear to me.
Answers: 1
![\bf \stackrel{f(x)}{y}=0.5(3)^x\qquad \stackrel{inverse}{\boxed{x}=0.5(3)^{\boxed{y}}} \\\\\\ log(x)=log[0.5(3)^y]\implies log(x)=log(0.5)+log[(3)^y] \\\\\\ log(x)-log(0.5)=log[(3)^y]\implies log(x)-log(0.5)=y\cdot log(3) \\\\\\ \cfrac{log(x)-log(0.5)}{log(3)}=\stackrel{f^{-1}(x)}{y}\\\\ -------------------------------\\\\ f^{-1}(7)=\cfrac{log(7)-log(0.5)}{log(3)}\implies f^{-1}(7)\approx 2.402173502732879697](/tpl/images/0145/8045/5dd8a.png)
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Given the function f(x) = 0.5(3)x, what is the value of f−1(7)? this question has been asked before...
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