THE QUESTION:
YOUR NAME: Carol
YOUR MATH COURSE (Algebra I, Geometry, Algebra II, other): Algebra I
YOUR MATH QUESTION (give the exact wording from your text or homework):
Let f(x) = x^2 - 1, and evaluate.
f(a) + f(3)
HAVE THE ANSWER (say, from the back of the book)? If so, put it here:
a^2 + 7
HONOR PLEDGE:
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this math question.
You'll hear back from me soon.
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THE RESPONSE:
PAYMENT CODE: #1
Hi Carol,
Let me show you the solution first,
and then I'll give you a bit of background, and point you to some more
explanation and practice on my web site.
f(x) = x^2 - 1
Replacing every "x" by "a":
f(a) = a^2 - 1
Replacing every "x" by "3":
f(3) = 3^2 - 1 = 9 - 1 = 8
Putting it all together:
f(a) + f(3)
= (a^2 - 1) + 8
= a^2 - 1 + 8
= a^2 + 7
Here are some things to remember:
f(x) = x^2 - 1 is function notation,
which gives you information about a rule (a "function" is just a rule).
Here, the NAME of the function is "f".
It's acting on an input, which is being called "x".
The number f(x) (read as "f of x") is the OUTPUT from the function f, when the input is x.
Thus, this rule is describing a function named f that
takes an input, squares it, and then subtracts 1.
You can think of the function "f" as a "box":
you drop an input "x" in the top of the box,
the function "f" DOES something to the input,
and the corresponding output "f(x)" drops out the bottom of the box.
If you want more explanation and help, try these web pages:
INTRODUCTION TO FUNCTION NOTATION:
http://www.onemathematicalcat.org/algebra_book/online_problems/function_notation.htm
MORE PRACTICE WITH FUNCTION NOTATION:
http://www.onemathematicalcat.org/algebra_book/online_problems/more_func_notation.htm
Thanks for the math question! I hope this solution is helpful.
If you need any further clarification on this question,
please insert "FOLLOW-UP QUESTION" in the subject line
of this email, and send it back to me.
There is no additional charge for a follow-up question.
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Dr. Carol J.V. Fisher
PO Box 912
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Have fun with math, and have a great day!
-- Dr. Fisher
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