Question

I am confused what does one to one mean.
ex. If the function is one to one find the inverse.
g(x)= square root( x+6),x is greater than our equal to -6

Answer 1

\[g(x)=\sqrt{x+6}\] and you want the inverse
put
\[x=\sqrt{y+6}\] and solve for \(y\)

Answer 2

you get
\[x^2=y+6\]\[x^2-6=y\] so
\[g^{-1}(x)=x^2-6\]

Answer 3

function is one to one means
a) it passes the "horizontal line test" or
b) if \(f(a)=f(b)\) then \(a=b\) in other words no two different inputs can give the same output