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Given the function f(x) = (2x+1)/(x-3), find the value of f⁻¹(3).

Mathematics

ScanSolve AI Answer

Answer

10
Graph of f(x) = (2x + 1)/(x − 3)

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Key points of f(x) = (2x + 1)/(x − 3)
Pointxy
x-intercept−0.50
y-intercept0−0.33

Step-by-step solution

4 steps

  1. To find f−1(3)f^{-1}(3), we need to find the value of xx for which f(x)=3f(x) = 3.

    Set the given function equal to 3:

    2x+1x−3=3\frac{2x+1}{x-3} = 3

  2. Multiply both sides by (x−3)(x-3) to eliminate the denominator.

    2x+1=3(x−3)2x+1 = 3(x-3)

  3. Distribute the 3 on the right side of the equation.

    2x+1=3x−92x+1 = 3x - 9

  4. Isolate xx by moving all xx terms to one side and constant terms to the other.

    Subtract 2x2x from both sides:

    1=3x−2x−91 = 3x - 2x - 9 1=x−91 = x - 9

    Add 9 to both sides:

    1+9=x1 + 9 = x x=10x = 10

    Therefore, f−1(3)=10f^{-1}(3) = 10.

    The final answer is 10.

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