Question

Match each function with the expression representing Its Inverse function.

Answer 1

Answer:

Step-by-step explanation:

1). g(x) = -0.5x

   Equation form of the given function is,

   y = -0.5x

 Interchange x and y,

  x = -0.5y

  Solve for y,

  y = $-\frac{x}{0.5}$

  y = -2x

  Inverse function will be,

  $g^{-1}x=-2x$

2). h(x) = 4x

   Equation form of the function will be,

   y = 4x

   Interchange x and y,

   x = 4y

   Solve for y,

   y = $\frac{x}{4}$

   Inverse function will be,

   $h^{-1}(x)=0.25x$

3). y = x - 4

    Interchange x and y,

    x = y - 4

    Solve for y,

    y = x + 4

    Therefore, inverse of the linear equation is,

    y = x + 4

4). f(x) = $\frac{x}{2}$

    Equation form of the function will be,

    y = $\frac{x}{2}$= x

     Interchange x and y,  

     x = $\frac{y}{2}$

    Solve for y,

     y = 2x

     Therefore, inverse function will be,

     $f^{-1}(x)=2x$

5). k(x) = x

     Equation form of the function will be,

     y = x

     Interchange x and y,

     x = y

     Solve for y,

     y = x

     Inverse of the function 'f' will be,

     $k^{-1}(x) =x$

6). p(x) = x + 4

     Equation form of the function will be,

     y = x + 4

     Interchange x and y,

     x = y + 4

     Solve for y,

     y = x - 4

     Inverse of the function 'p' will be,

     $p^{-1}(x)=x - 4$