Question

is f(x) = 3root2x-1 a rational function, as well as a polynomial function? (I know it's radical.

Answer 1

oh it's one to one as well right?

Answer 2

oh and how the heck to do I solve for it's inverse 0.0 s

Answer 3

I'm assuming that it's \[f(x)=3\sqrt{2x-1}\] This is a radical function (since it has a radical in it), but it is NOT rational (since it's not a ratio of two polynomials).


This function is one-to-one and you can show that by proving that f(x)=f(y) <--> x = y


Finding the inverse:

\[\large f(x)=3\sqrt{2x-1}\]

\[\large y=3\sqrt{2x-1}\]

\[\large x=3\sqrt{2y-1}\]

\[\large \frac{x}{3}=\sqrt{2y-1}\]

\[\large \frac{x^2}{9}=2y-1\]

\[\large \frac{x^2}{9}+1=2y\]

\[\large \frac{x^2+9}{9}=2y\]

\[\large \frac{x^2+9}{18}=y\]

\[\large y=\frac{x^2+9}{18}\]

So the inverse is \[\large f^{-1}(x)=\frac{x^2+9}{18}\]