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

What is the inverse of the function\newlineg(x)=5(x−2)?g−1(x)= \begin{array}{l} g(x)=5(x-2) ? \\ g^{-1}(x)= \end{array}

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Q. What is the inverse of the function\newlineg(x)=5(x−2)?g−1(x)= \begin{array}{l} g(x)=5(x-2) ? \\ g^{-1}(x)= \end{array}
  1. Rewrite function with y: To find the inverse of the function g(x)=5(x−2)g(x) = 5(x - 2), we need to switch the roles of xx and yy and then solve for yy. Let's start by rewriting the function with yy instead of g(x)g(x):\newliney=5(x−2)y = 5(x - 2)
  2. Switch x and y: Now, we switch x and y to find the inverse:\newlinex=5(y−2)x = 5(y - 2)
  3. Isolate term with y: Next, we solve for y. Start by dividing both sides of the equation by 55 to isolate the term with y:\newlinex5=y−2\frac{x}{5} = y - 2
  4. Solve for y: Now, add 22 to both sides of the equation to solve for yy:\newliney=x5+2y = \frac{x}{5} + 2\newlineThis is the inverse function of g(x)g(x).

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