SOLUTION: f(x) = 3x + 2, find f(x+5)

SOLUTION: f(x) = 3x + 2, find f(x+5) - f(5)

Question 655034: f(x) = 3x + 2, find f(x+5) - f(5)

Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
You must understand what the symbol for function means.
In your case you have,f(x), where f() is the name of the function and the contents of the parenthesis is called the argument, in your case the argument is x. The name defines what is called the topology of the function, that is, in your case, 3x+2 or
(1) f(x) = 3x + 2
Now to evaluate the function for a specific value of x, say x = 7, we write
(2) f(7) = 3*7 + 2, where we simply substitute into the expression for the function the value of x given by the argument, 7, in this example.
Now evaluate (2) and get
(3) f(7) = 23.
Now to use your problem, we want f(x+5), so where ever x appears in the expression of f(), we replace it with the whole new argument. x+5, in this case, and get
(4) f(x+5) = 3*(x+5) + 2 which simplifies to
(5) f(x+5) = 3x + 17
Now the next evaluation you want is f(5), or
(6) f(5) = 3*5 + 2 or
(7) f(5) = 17
Your problem is to find the difference which I will call D, f(x+5)-f(5) or (5) minus (7), giving
(8) D = f(x+5) - f(5) or
(9) D = (3x+17) - (17) or
(10) D = 3x + 17 - 17 or
(11) D = 3x
Answer: The difference between f(x+5) and f(5) is 3x.
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