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What is the inverse of the function {:[g(x)=-(2)/(5)x+3?],[g^(-1)(x)=]:}

What is the inverse of the function g(x)=−25x+3 g(x) = -\frac{2}{5}x + 3 ? g−1(x)= g^{-1}(x) =

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Q. What is the inverse of the function g(x)=−25x+3 g(x) = -\frac{2}{5}x + 3 ? g−1(x)= g^{-1}(x) =
  1. Rewriting the function: To find the inverse of the function g(x)=−(25)x+3g(x) = -\left(\frac{2}{5}\right)x + 3, 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=−(25)x+3y = -\left(\frac{2}{5}\right)x + 3
  2. Switching x and y: Now, we switch x and y to find the inverse: x=−(25)y+3x = -\left(\frac{2}{5}\right)y + 3
  3. Moving the constant term: Next, we solve for y. Start by moving the constant term to the other side:\newlinex−3=−(25)yx - 3 = -\left(\frac{2}{5}\right)y
  4. Isolating y: Now, we multiply both sides by −52-\frac{5}{2} to isolate y:\newliney = −52-\frac{5}{2}(x - 33)
  5. Distributing the coefficient: Distribute the −52-\frac{5}{2} across the parentheses:\newliney = −52-\frac{5}{2}x + 152\frac{15}{2}
  6. Finding the inverse function: We have now found the inverse function, which we can denote as g−1(x)g^{-1}(x):\newlineg−1(x)=(−52)x+(152)g^{-1}(x) = \left(-\frac{5}{2}\right)x + \left(\frac{15}{2}\right)

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