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What is the inverse of the function {:[f(x)=-6x-7?],[f^(-1)(x)=]:}

What is the inverse of the function f(x)=−6x−7 f(x) = -6x - 7 ? f−1(x)= f^{-1}(x) =

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Q. What is the inverse of the function f(x)=−6x−7 f(x) = -6x - 7 ? f−1(x)= f^{-1}(x) =
  1. Replace f(x)f(x) with yy: To find the inverse of the function f(x)=−6x−7f(x) = -6x - 7, we first replace f(x)f(x) with yy to make the equation easier to manipulate.\newliney=−6x−7y = -6x - 7
  2. Swap roles of x and y: Next, we swap the roles of x and y to find the inverse function. This means we replace yy with xx and xx with yy in the equation.x=−6y−7x = -6y - 7
  3. Solve for y: Now, we need to solve for y to get the inverse function. We start by adding 77 to both sides of the equation to isolate the term with y.\newlinex+7=−6yx + 7 = -6y
  4. Divide both sides by −6 -6 : Next, we divide both sides of the equation by −6 -6 to solve for y y . y=x+7−6 y = \frac{x + 7}{-6} or y=−16x−76 y = -\frac{1}{6} x - \frac{7}{6}
  5. Inverse function found: We have found the inverse function. We replace yy with f−1(x)f^{-1}(x) to denote the inverse function of f(x)f(x).\newlinef−1(x)=−16x−76f^{-1}(x) = -\frac{1}{6} x - \frac{7}{6}

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