What is the inverse of the function {:[g(x)=5(x-2)?],[g^(-1)(x)=]:}

Rewrite function with y: To find the inverse of the function g(x) = 5(x - 2), we need to switch the roles of x and y and then solve for y. Let's start by rewriting the function with y instead of g(x): y = 5(x - 2)Switch x and y: Now, we switch x and y to find the inverse: x = 5(y - 2)Isolate term with y: Next, we solve for y. Start by dividing both sides of the equation by 5 to isolate the term with y: x/5 = y - 2Solve for y: Now, add 2 to both sides of the equation to solve for y: y = x/5 + 2 This is the inverse function of g(x).

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Q. What is the inverse of the function

\newline

\begin{array}{l} g(x)=5(x-2) ? \\ g^{-1}(x)= \end{array}

Rewrite function with y: To find the inverse of the function $g(x) = 5(x - 2)$ , we need to switch the roles of $x$ and $y$ and then solve for $y$ . Let's start by rewriting the function with $y$ instead of $g(x)$ : $\newline$ $y = 5(x - 2)$
Switch x and y: Now, we switch x and y to find the inverse: $\newline$ $x = 5(y - 2)$
Isolate term with y: Next, we solve for y. Start by dividing both sides of the equation by $5$ to isolate the term with y: $\newline$ $\frac{x}{5} = y - 2$
Solve for y: Now, add $2$ to both sides of the equation to solve for $y$ : $\newline$ $y = \frac{x}{5} + 2$ $\newline$ This is the inverse function of $g(x)$ .