Question

Arthur has decided to start saving for a new computer. His money is currently in a piggy bank at home, modeled by the function s(x) = 85. He was told that he could do the laundry for the house and his allowance would be a(x) = 10(x − 1), where x is measured in weeks. Explain to Arthur how he can create a function that combines the two, and describe any simplification that can be done.

Answer 1

Two or more independent functions (say f(x) and g(x)) can be combined to generate a new function (say g(x)) using any of the following approach.

$h(x) = f(x) + g(x)$         $h(x) = f(x) - g(x)$

$h(x) = \frac{f(x)}{g(x)}$                   $h(x) = f(g(x))$

And many more.

The approach or formula to use depends on the question.

In this case, the combined function is:

$f(x) = 75+ 10x$

The savings function is given as

$s(x) = 85$

The allowance function is given as:

$a(x) = 10(x - 1)$

The new function that combined his savings and his allowances is calculated as:

$f(x) = s(x) + a(x)$

Substitute values for s(x) and a(x)

$f(x) = 85 + 10(x - 1)$

Open bracket

$f(x) = 85 + 10x - 10$

Collect like terms

$f(x) = 85 - 10+ 10x$

$f(x) = 75+ 10x$

Read more about functions at:

brainly.com/question/15458447

Answer 2

Answer:

For future help Here is the answer.  

So s(x)=85 is how much money he has in his piggy bank, and a(x)=10(x-1) is his allowance he gets every week.  We are going to make a new equation for this.  The new Equation will be f(x)=s(x)+a(x).  Now we put the answer we have in this new equation, and we get  g(x)=85+ 10(x-1).

Step-by-step explanation: