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Math Help - function inverses

  1. #1
    Senior Member euclid2's Avatar
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    function inverses

    1. Find the equation of the inverse for each function. State which of the following inverses are functions.
    2. a. f(x) = 1/2 x - 3
    3. b. f(x) = 4x 2 - 5
      c. A(r) = 4(Pi)r2
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by euclid2 View Post
    1. Find the equation of the inverse for each function. State which of the following inverses are functions.
    2. a. f(x) = 1/2 x - 3
    3. b. f(x) = 4x 2 - 5
      c. A(r) = 4(Pi)r2
    a) First, write the equation as

    y=\frac{x}{2}-3

    Interchange the x and y.

    x=\frac{y}{2}-3

    Solve for y.

    2x=y-6

    y=2x+6

    f^{-1}(x)=2x+6

    The inverse is also a linear function.

    b) Follow same procedure as (a) above.

    f(x)=y=4x^2-5

    x=4y^2-5

    4y^2=x+5

    y^2=\frac{x+5}{4}

    y=f^{-1}(x)=\pm\frac{\sqrt{x+5}}{2}

    This inverse is not a function because any acceptable value of domain x yields two values for range y.

    c) Follow same procedure as (a) above.

    A(r)=y=4\pi r^2

    r=4\pi y^2

    y^2=\frac{r}{4\pi}

    y=A^{-1}(r)=\pm\frac{1}{2}\sqrt{\frac{r}{\pi}}

    This inverse is not a fraction because any acceptable value of domain r yields 2 values for range y.
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