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What is the inverse of the function {:[f(x)=8x+1?],[f^(-1)(x)=]:}

What is the inverse of the function f(x)=8x+1 f(x)=8x+1 ? f−1(x)= f^{-1}(x)=

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Q. What is the inverse of the function f(x)=8x+1 f(x)=8x+1 ? f−1(x)= f^{-1}(x)=
  1. Replace f(x)f(x) with yy: To find the inverse of the function f(x)=8x+1f(x) = 8x + 1, 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:y=8x+1y = 8x + 1
  2. Isolate xx on one side: Next, we need to isolate xx on one side of the equation. To do this, we first subtract 11 from both sides of the equation:\newliney−1=8xy - 1 = 8x
  3. Divide both sides by 88: Now, we divide both sides of the equation by 88 to solve for x:\newlinex=y−18x = \frac{y - 1}{8}
  4. Replace yy with f−1(x)f^{-1}(x): The expression we have for xx is the inverse function of f(x)f(x), but we need to replace yy with the inverse notation f−1(x)f^{-1}(x) to complete the process:\newlinef−1(x)=x−18f^{-1}(x) = \frac{x - 1}{8}

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