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If f(x) = 5x, what is f–1(x)?

User Lokkio
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{f}^( - 1) (x) = switching \: the \: x \: for \\ the \: y \\ f(x) = 5x - - > x = 5y \\ solve \: for \: y. \: {f}^( - 1) (x) = (x)/(5)
User Flavio Caduff
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4 votes

Answer:


f^(-1)(x)=(x)/(5)

Explanation:


f^(-1)(x) is the inverse function of
f(x), that is, if
f(x) transform "a" to "b", then
f^(-1)(x) transform "b" to "a".

thus:


f(x)= 5x\\\\y = 5x \ \ \ \ \ \ \ \ \ \ \ Making \ f(x)=y \\\\(y)/(5)= x \ \ \ \ \ \ \ \ \ \ \ divide \ both \ sides \ by \ 5\\\\x=(y)/(5) \\\\so \ f^(-1)(y) =(y)/(5)\\\\

due to the choice of variable is arbitrary, we can write this like:


f^(-1)(x)=(x)/(5)

User Platzhersh
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