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Given f^(-1)(x)=6x+7, Find f.

88. Given f−1(x)=6x+7 f^{-1}(x)=6 x+7 , Find f f .

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Full solution

Q. 88. Given f−1(x)=6x+7 f^{-1}(x)=6 x+7 , Find f f .
  1. Express xx in terms of yy: To find ff, we need to express xx in terms of yy from the equation y=6x+7y = 6x + 7. Let y=f−1(x)y = f^{-1}(x), then x=f(y)x = f(y). So, we have x=6y+7x = 6y + 7.
  2. Solve for y: Now, we need to solve for yy in terms of xx.\newlineSubtract 77 from both sides to isolate the term with yy.\newlinex−7=6yx - 7 = 6y.
  3. Divide both sides: Divide both sides by 66 to solve for yy.y=x−76.y = \frac{x - 7}{6}.
  4. Write function f: Since y=f(x)y = f(x), we can write the function f as:\newlinef(x)=x−76f(x) = \frac{x - 7}{6}.

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