Given the coordinates for the function below, which of the following arecoordinates for its inverse?Gallons

Given the coordinates for the function below, which of the following are coordinates for its inverse?
Gallons Cost, in
of Gas Dollars
1
2
5
15
20
1.25
2.50
6.25
18.75
25.00

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This Post Has 5 Comments

  1. The equation of the function is assumed to be a straight line is of the form,

    [tex]y= mx+c[/tex],  where  [tex]m,c[/tex]

    are the gradient and the y intercept respectively.

    The gradient is computed using the formula for the gradient, i.e

    [tex]m=\frac{y_2-y_1}{x_2-x_1} = \frac{-5-5}{2-0} = -5[/tex].

    The equation of the line is,

    [tex]y= -5x+c\\=5=-5(0)+c\\= c= 5[/tex]

    The equation of the function is ,

    [tex]y = -5x+5.[/tex].

    The value of the x-coordinate when the y coordinate is 0 is found as shown below.

    [tex]0=-5x+5\\=x=1\\[/tex].

    so the x-coordinate is 1.

  2. g(x) = 0.8x  gal/dollar

    Step-by-step explanation:

    This is a direct relation, each gallon costs 1.25, 20 gal. costs 25.00, etc.

    so

    f(x) = 1.25x  where x = number of gal.  f(x) is the cost

    The inverse relation is the reciprocal,

    for each $1.00, we can buy 1/1.25 = 0.8 gal.

    or

    g(x) = 0.8x  where x = amount, g(x) is number of gallons

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