Question

If f(x)=(1/9x)-2 , what is f^–1(x)?

Answer 1

I hope this helps you



y= (1x/9)-2



y+2=1x/9


9(y+2)= x


f^-1 (x)= 9 (x+2)


?



y=1/9x -2


y+2= 1/9x



x= 1/9 (y+2)



f^-1 (x)= 1/9 (x+2)

Answer 2

`f^(-1)(x)=(1)/(9(x+2))`

Explanation:

We have to find the inverse of the given function
`f(x)=(1)/(9x)-2`

1). We will rewrite the function in the form of a equation.

`y=(1)/(9x)-2`

2). Now we flip y by x and solve the equation for y.

`x=(1)/(9y)-2`

`x+2=(1)/(9y)`

`9y(x+2)=1` [ By cross multiplication]

`9y=(1)/((x+2))`

`y=(1)/(9(x+2))`

3). Now we rewrite the equation in the form of a function.

`f^(-1)(x)=(1)/(9(x+2))`

Therefore, the answer is
`f^(-1)(x)=(1)/(9(x+2))`