What is the inverse of the function {:[g(x)=(7x+3)/(x-5)?],[g^(-1)(x)=◻]:}

Understand Inverse Function: Understand the concept of finding an inverse function. To find the inverse of a function, we need to swap the x and y variables and then solve for y. This process will give us the inverse function, denoted as g^(-1)(x).Original Function with y: Write the original function with y instead of g(x). y = (7x + 3) / (x - 5)Swap Variables: Swap the x and y variables to begin finding the inverse. x = (7y + 3) / (y - 5)Eliminate Fraction: Multiply both sides by (y - 5) to eliminate the fraction. x(y - 5) = 7y + 3Combine Terms: Distribute x on the left side of the equation. xy - 5x = 7y + 3Factor Out y: Get all terms containing y on one side and the constant terms on the other side. xy - 7y = 5x + 3Solve for y: Factor out y from the left side of the equation. y(x - 7) = 5x + 3Divide both sides by (x - 7) to solve for y. y = (5x + 3) / (x - 7)

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What is the inverse of the function $g(x) = \frac{7x+3}{x-5}$ ? $\newline$ $g^{-1}(x) = \square$

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Q. What is the inverse of the function

g(x) = \frac{7x+3}{x-5}

\newline

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

Understand Inverse Function: Understand the concept of finding an inverse function. To find the inverse of a function, we need to swap the $x$ and $y$ variables and then solve for $y$ . This process will give us the inverse function, denoted as $g^{-1}(x)$ .
Original Function with y: Write the original function with $y$ instead of $g(x)$ . $\newline$ $y = \frac{7x + 3}{x - 5}$
Swap Variables: Swap the $x$ and $y$ variables to begin finding the inverse. $x = \frac{7y + 3}{y - 5}$
Eliminate Fraction: Multiply both sides by $(y - 5)$ to eliminate the fraction. $x(y - 5) = 7y + 3$
Combine Terms: Distribute $x$ on the left side of the equation. $\newline$ $xy - 5x = 7y + 3$
Factor Out $y$ : Get all terms containing $y$ on one side and the constant terms on the other side. $\newline$ $xy - 7y = 5x + 3$
Solve for $y$ : Factor out $y$ from the left side of the equation. $y(x - 7) = 5x + 3$
Solve for y: Factor out $y$ from the left side of the equation. $\newline$ $y(x - 7) = 5x + 3$ Divide both sides by $(x - 7)$ to solve for $y$ . $\newline$ $y = \frac{5x + 3}{x - 7}$