Answered

Get reliable answers to your questions at Westonci.ca, where our knowledgeable community is always ready to help. Experience the convenience of getting reliable answers to your questions from a vast network of knowledgeable experts. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

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 our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.