Question

I am mucho of the confused. How do inverse functions?

Given f(x) = the quantity of 5x plus 1, divided by 2 solve for f^-1(8).

Answer 1

\(\bf f(x)={\color{red}{ y}}=\cfrac{5{\color{blue}{ x}}+1}{2}\qquad inverse\implies {\color{blue}{ x}}=\cfrac{5{\color{red}{ y}}+1}{2}\Leftarrow f^{-1}(x)\)

as you can see, to get the inverse relation, we simply swap about the variables
then solve for "y"

Answer 2

How do you solve for y like that then? I mean like... Do you end up multiplying by 2, to then get 10y+2 and then -2 from each side.. Or like, what...?

Answer 3

well, yes you do end up multiplying by 2 first
then subtract 1 from both sides
then divide by 5

Answer 4

2(5y+1)
10y+2??

Answer 5

\(\bf x=\cfrac{5y+1}{2}\implies 2x=5y+1\implies 2x-1=5y\\ \quad \\\implies \cfrac{2x-1}{5}=y\Leftarrow f^{-1}(x)\)

Answer 6

\(\bf f^{-1}({\color{red}{ 8}})=\cfrac{2({\color{red}{ 8}})-1}{5}\)

Answer 7

OOoooohhhhh, I understand it now-- Thank you very much!!

Answer 8

yw