Answered

Find the best answers to your questions at Westonci.ca, where experts and enthusiasts provide accurate, reliable information. Discover precise answers to your questions from a wide range of experts on our user-friendly Q&A platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

Find The Algebraic Inverse.
f(x)=15x-1

Sagot :

Hippalectryon
We want a function [tex]g[/tex] such that [tex]g(15x-1)=x[/tex]

One easy way to do to that is to choose [tex]g(x)=\dfrac{x+1}{15}[/tex]

That function works : [tex]g(15x-1)=\dfrac{15x-1+1}{15}=x[/tex]

Due to the uniqueness of the inverse, this is the function we were searching for.
[tex]f(x)=15x-1\to y=15x-1\\\\15x-1=y\ \ \ \ |add\ 1\ to\ both\ sides\\\\15x=y+1\ \ \ \ \ |divide\ both\ sides\ by\ 15\\\\\boxed{x=\frac{y}{15}+\frac{1}{15}}\to\boxed{x=\frac{1}{15}y+\frac{1}{15}}\\\\Answer:\boxed{\boxed{[f(x)]^{-1}=\frac{1}{15}x+\frac{1}{15}}}[/tex]
We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.