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