Find the inverse of function f.
f(x)=9x+7
A. f^-1(x)=x-9-7
B. f^-1(x)=7/9x-1/9
C. f^-1(x)=7x+9
D. f^-1(x)=1/9x-7/9
To find the inverse of the function \(f(x) = 9x + 7\), we swap the positions of \(x\) and \(f(x)\) and solve for \(x\). So, we have \(x = 9f^{-1}(x) + 7\).
Now, let's solve for \(f^{-1}(x)\):
\(x - 7 = 9f^{-1}(x)\).
\(\dfrac{x - 7}{9} = f^{-1}(x)\).
So, the inverse of the function is \(f^{-1}(x) = \dfrac{x - 7}{9}\).
Therefore, the correct answer is B. \(f^{-1}(x) = \dfrac{7}{9}x - \dfrac{1}{9}\).