Question

Express the inverse of f(x)=6x-1 in the form y = f^-1(x)

Answer 1

Inverse: Take the x and the y and switch them.

We can assume that f(x) = y and therefore the equation can be written as:

y=6x-1

Swapping the x and y gives us:

x=6y-1

Now solve for y.

Answer 2

y=1/6 + x/6?

Answer 3

Similar Example:


Find the inverse of \[\Large f(x) = 9x + 20\]


Basic Idea: Replace f(x) with y. Swap x and y, then solve for y. After getting y isolated, replace y with \(\Large f^{-1}(x)\) to get the inverse function.


\[\Large f(x) = 9x + 20\]


\[\Large y = 9x + 20\]


\[\Large x = 9y + 20\]


\[\Large x - 20 = 9y\]


\[\Large 9y = x - 20\]


\[\Large y = \frac{x - 20}{9}\]


\[\Large f^{-1}(x) = \frac{x - 20}{9}\]


So the inverse function is \[\Large f^{-1}(x) = \frac{x - 20}{9}\]


Keep in mind that this is NOT your answer as it's only an example.

Answer 4

f^(-1) (x) = x+1/6?

Answer 5

if you mean \[\Large f^{-1}(x) = \frac{x+1}{6}\]

then you are 100% correct

Answer 6

yes!!!

Answer 7

:)