F(x)=x^2-10 and g(x)=7–x, find (f-g)(-6)

1 answer:

3 0

$(f-g)(x)=f(x)-g(x)\\\\f(x)=x^2-10\\\\f(-6)\to\text{put x = -6 to the equation}\\\\f(-6)=(-6)^2-10=36-10=26\\\\g(x)=7-x\\\\g(-6)\to\text{put x = -6 to the equation}\\\\g(-6)=7-(-6)=7+6=13\\\\(f-g)(-6)=f(-6)-g(-6)=26-13=13$

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At one gym, there is a $12 start-up fee, and after that each month at the gym costs $20. At another gym, it costs $4 to startup,

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Answer:

In 4 months the cost of both gyms will be the same.

Step-by-step explanation:

At first we need to model the function to calculate the cost of the 2 gyms.

Slope-intercept equation of linear function

$f(x)=mx+b$

where

$m\rightarrow$ slope of line

$b\rightarrow$ y-intercept

Let linear function to calculate total cost of gym be:

$c(n)=mn+b$

where

$c\rightarrow$ total cost of gym

$m\rightarrow$ cost per month (slope)

$n\rightarrow$ number of months

$b\rightarrow$ start-up fee (y-intercept)

For Gym 1

$m=20$ , $b=12$

$c(n)=20n+12$

For Gym 2

$m=22$ , $b=4$

$c(n)=22n+4$

In order to find the number of months the cost of both gyms will be the same, we need to equate both functions and solve for number of months $(n)$

$20n+12=22n+4$

$\\\textrm{Subtracting 22n from both sides}\\20n-22n+12=22n-22n+4\\-2n+12=4\\\textrm{Subtracting 12 from both sides}\\-2n+12-12=4-12\\-2n=-8\\\textrm{Dividing both sides by -2}\\\frac{-2}{-2}n=\frac{-8}{-2}\\n=4\textrm{ months}$