begin{array}{l}text { Let } f(x)=frac{x+1}{x+9} f^{-1}(-10)=end{array}

Question

begin{array}{l}text { Let }  f(x)=frac{x+1}{x+9}  f^{-1}(-10)=end{array}

Accepted Answer

Step:1 ：Let the function be (f(x)=frac{x+1}{x+9}).Step:2 ：To find the inverse of a function, we need to switch the x and y (or f(x)) values. This means we set x = f(y) and solve for y.Step:3 ：In this case, we need to find the value of x such that (f(x) = -10).Step:4 ：Once we have the value of x, we can substitute it into the inverse function to find the value of (f^{-1}(-10)).Step:5 ：Solving the equation (frac{x + 1}{x + 9} = -10), we find that x = -frac{91}{11}.Step:6 ：Therefore, the solution to the equation is (f^{-1}(-10) = boxed{-frac{91}{11}}).

Answer

Step: 1 ：Let the function be (f(x)=frac{x+1}{x+9}).Step: 2 ：To find the inverse of a function, we need to switch the x and y (or f(x)) values. This means we set x = f(y) and solve for y.Step: 3 ：In this case, we need to find the value of x such that (f(x) = -10).Step: 4 ：Once we have the value of x, we can substitute it into the inverse function to find the value of (f^{-1}(-10)).Step: 5 ：Solving the equation (frac{x + 1}{x + 9} = -10), we find that x = -frac{91}{11}.Step: 6 ：Therefore, the solution to the equation is (f^{-1}(-10) = boxed{-frac{91}{11}}).

$\begin{array}{l}\text { Let } \\ f(x)=\frac{x+1}{x+9} \\ f^{-1}(-10)=\end{array}$

Answer

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