Respuesta :
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)
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:
[tex]f^{-1}(x)=\frac{1}{9(x+2)}[/tex]
Step-by-step explanation:
We have to find the inverse of the given function [tex]f(x)=\frac{1}{9x}-2[/tex]
1). We will rewrite the function in the form of a equation.
[tex]y=\frac{1}{9x}-2[/tex]
2). Now we flip y by x and solve the equation for y.
[tex]x=\frac{1}{9y}-2[/tex]
[tex]x+2=\frac{1}{9y}[/tex]
[tex]9y(x+2)=1[/tex] [ By cross multiplication]
[tex]9y=\frac{1}{(x+2)}[/tex]
[tex]y=\frac{1}{9(x+2)}[/tex]
3). Now we rewrite the equation in the form of a function.
[tex]f^{-1}(x)=\frac{1}{9(x+2)}[/tex]
Therefore, the answer is [tex]f^{-1}(x)=\frac{1}{9(x+2)}[/tex]
