Answer:
Step-by-step explanation:
First, let's rewrite the original function:
ƒ(<em>x</em>) = 5(<em>x</em> – 3) + 17
This could easily be simplified, which might make it easier:
ƒ(<em>x</em>) = 5<em>x</em> – 15 + 17 — distribute the 5 to (<em>x</em> – 3)
ƒ(<em>x</em>) = 5<em>x</em> + 2 — simplify
That looks easier to solve, doesn't it? Now, let's substitute 12 for <em>x</em> and solve for ƒ(12) [this is another way of writing <em>x</em> = 12]
ƒ(12) = 5(12) + 2 — substitute 12 for <em>x</em>
ƒ(12) = 60 + 2 — multiply and simplify
ƒ(12) = 62 — add and simplify
Now, let's prove this method works by substituting 12 for <em>x</em> in the original function:
ƒ(<em>x</em>) = 5(<em>x</em> – 3) + 17 — original function
ƒ(12) = 5(12 – 3) + 17 — substitute 12 for <em>x</em>
ƒ(12) = 5(9) + 17 — here, I <em>subtracted</em> the numbers in the parentheses
ƒ(12) = 45 + 17 — simplify by multiplying 5 and 9
ƒ(12) = 55 + 7 — rewriting to make mental addition easier
ƒ(12) = 60 + 2 — rewriting to make mental addition easier; does this look familiar?
ƒ(12) = 62 — simplifying to find final answer
That's just one way of breaking up the numbers so they're easier to add. You could just use a calculator, but I did this in my head, so…
There's two more ways to use the original function to solve for ƒ(12), and it's these methods:
<u>Method 1</u>
ƒ(<em>x</em>) = 5(<em>x</em> – 3) + 17 — original function
ƒ(12) = 5(12 – 3) + 17 — substitute 12 for <em>x</em>
ƒ(12) = 60 – 15 + 17 — here, I <em>distributed 5 to each term </em><u><em>before</em></u><em> doing anything else</em>
ƒ(12) = 45 + 17 — simplifying by subtracting 15 from 60
ƒ(12) = 62 — simplifying; we get the same answer
<u>Method 2</u>
ƒ(<em>x</em>) = 5(<em>x</em> – 3) + 17 — original function
ƒ(12) = 5(12 – 3) + 17 — substitute 12 for <em>x</em>
ƒ(12) = 60 – 15 + 17 — here, I <em>distributed 5 to each term </em><u><em>before</em></u><em> doing anything else</em>
ƒ(12) = 60 + 2 — simplifying by subtracting 15 from 17
ƒ(12) = 62 — simplifying; we get the same answer
What happens every time? We get the same answer, <u>ƒ(12) = 62</u>! To boot, sometimes you can use a rule of three to prove something true: if something happens 3 times, it will be true. Of course, you probably won't have time to do all this. I did so to help you understand the concept better. By the way, the last two methods don't follow the order of operations, P.E.M.D.A.S. (operations in parentheses; exponents; multiplication; division; addition; subtraction). That's a heads-up in case you get an order of operations question so you don't make a mistake.
I hope this helps you! Have a great day!
