A season pass to an amusement park costs $70 per family member plus an additional $50 fee for parking. The function C(x)=70x+50 represents t

Question

A season pass to an amusement park costs $70 per family member plus an additional $50 fee for parking. The function C(x)=70x+50 represents the total cost of the season pass for a family, where x is the number of family members on the season pass. Find the inverse function. (show workings)

Write the equation in slope-intercept form. y+5=−6(x+7)

i need answers to these in 10 minutes.

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Vodka 3 months 2021-08-18T06:19:54+00:00 1 Answers 7 views 0

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    2021-08-18T06:21:53+00:00

    Answer:

    a) The inverse is g(x) = (1/70)*x – 50/70

    b) The slope intercept form is y = -6*x – 47

    Step-by-step explanation:

    a) When we have a function f(x), the inverse of this function (let’s call it g(x)) is such that:

    g(f(x)) = x

    f(g(x)) = x

    for every x.

    In this case, we have:

    f(x) = 70*x + 50

    This is a linear function, and the inverse will be also a linear function.

    Then the inverse will be something like:

    g(x) = a*x + b

    then:

    g( f(x)) = x = a*( 70*x + 50) + b

    then we can just solve the equation:

    x = a*( 70*x + 50) + b

    x = a*70*x + a*50 + b

    If we separate terms by the powers of x in each side of the equation, we have:

    1*x + 0*x^0 = (a*70)*x + (a*50 + b)*x^0

    (where x^0 = 1)

    then:

    1 = (a*70)

    a = 1/70

    and:

    0 =  (a*50 + b)

    0 = 50/70 + b

    -50/70 = b

    Then the inverse of f(x) is:

    g(x) = (1/70)*x – 50/70.

    b) The slop-intercept form of a linear equation is:

    y = a*x + b

    where a is the slope, and b is the y-intercept.

    We want to write in this form the equation:

    y + 5 = -6*(x + 7)

    The first step is to isolate the “y” in one side of the equation:

    y = -6*(x + 7) – 5

    Now let’s simplify the right side:

    y = -6*x – 6*7 – 5

    y = -6*x – 42 – 5

    y = -6*x – 47

    This is the slope-intercept form, where the slope is -6, and the y-intercept is -42.

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