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.

Answer 1

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.