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

What is the inverse of the function f(x)=3x−2 f(x)=3x-2 ? f−1(x)= f^{-1}(x)=

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Q. What is the inverse of the function f(x)=3x−2 f(x)=3x-2 ? f−1(x)= f^{-1}(x)=
  1. Replace f(x)f(x) with yy: To find the inverse of the function f(x)=3x−2f(x) = 3x - 2, we need to solve for xx in terms of yy, where y=f(x)y = f(x). We start by replacing f(x)f(x) with yy:\newliney=3x−2y = 3x - 2
  2. Isolate x on one side: Next, we need to isolate x on one side of the equation. To do this, we'll add 22 to both sides of the equation:\newliney + 22 = 33x - 22 + 22\newliney + 22 = 33x
  3. Divide both sides by 33: Now, we divide both sides of the equation by 33 to solve for x: (y+2)/3=x(y + 2) / 3 = x
  4. Inverse function of f(x)f(x): The expression we have for xx is the inverse function of f(x)f(x). We denote the inverse function as f−1(x)f^{-1}(x), so we have:\newlinef−1(x)=x+23f^{-1}(x) = \frac{x + 2}{3}

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