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$What is the inverse of the function {:[f(x)=-6x-7?],[f^(-1)(x)=◻]:}$

What is the inverse of the function $f(x) = -6x - 7$ ? $f^{-1}(x) = \square$

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Find the vertex of the transformed function

Full solution

Q. What is the inverse of the function

f(x) = -6x - 7

?

f^{-1}(x) = \square

Understand Inverse Function: Understand the concept of an inverse function. $\newline$ The inverse function, denoted as $f^{-1}(x)$ , swaps the roles of the input and output of the original function $f(x)$ . To find the inverse, we solve for $x$ in terms of $y$ and then swap $x$ and $y$ .
Write Original Function: Write the original function with $y$ instead of $f(x)$ . $\newline$ $y = -6x - 7$
Swap Variables: Swap $x$ and $y$ to begin finding the inverse. $\newline$ $x = -6y - 7$
Solve for Inverse: Solve for $y$ to find the inverse function. $\newline$ Add $7$ to both sides of the equation: $\newline$ $x + 7 = -6y$ $\newline$ Now, divide both sides by $-6$ to solve for $y$ : $\newline$ $y = \frac{x + 7}{-6}$
Write Inverse Function: Write the inverse function. $\newline$ The inverse function is $f^{-1}(x) = \frac{x + 7}{-6}$ .

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