Solve the equation. 30- (x + 5) = 7x-7 The solution is x =
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Every function is a rule which tells you how to associate inputs and outputs. The input, also known as independent variable, is often indicated with the letter , while the output, also known as dependent variable, is often indicated with the letter
.
With this notation, we write , read "y is a function of x", in the sense that the value of the variable y depends on the value of the variable x, and f is the function that tells you how y depends on x.
In your example, you have , which means "subtract four times the input (4x) from 2"
So, it doesn't matter which input you chose (i.e. the value for x), because you will always have to behave this way:
- Pick an input value, x
- Multiply it by four to get 4x
- Subtract this number from 2: 2-4x
Here are some examples of explicit calculations: if I choose and input, the workflow will be
- Pick an input value, 2
- Multiply it by four to get 8
- Subtract this number from 2: 2-8=-6
So, if the input is 2, the output is -6
Similarly, if we choose as input, we have:
- Pick an input value, 0
- Multiply it by four to get 0
- Subtract this number from 2: 2-0=2
So, if the input is 0, the output is 2. And so on: for every possible value for x you have the correspondant value for y, with the function f telling you how to associate one with the other.
Odd numbers take the form , where
is an integer. When
, the last odd number would be 799. So we're adding
By reversing the order of terms, we have
and we can pair up terms in both sums at the same position to write
so that we are basically adding 400 copies of 800, and from there we can find the value of the sum right away:
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We could also make use of the formulas,
We have