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1998

JEE Main 1998 Mathematics question on Sets Relations and Functions

If f(x)=3x−5f(x) = 3x - 5, then f−1(x)f^{-1}(x)
  1. A.
    is given by 13x−5\dfrac{1}{3x-5}
  2. B.
    is given by x+53\dfrac{x+5}{3}
  3. C.
    does not exist because ff is not one-one
  4. D.
    does not exist because ff is not onto
Show answer and solution

Correct option: B

Solution

To find f⁻¹(x), set y = 3x - 5, then solve for x: x = (y + 5)/3, so f⁻¹(x) = (x + 5)/3. Since f is a linear function with non-zero slope, it is both one-one (strictly increasing) and onto ℝ, so the inverse exists and is given by option 2.

[1998]

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