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Doss [256]
2 years ago
11

HELP MEEEE How do you add and subtract functions?

Mathematics
2 answers:
nata0808 [166]2 years ago
5 0

Answer:

To add or subtract functions, just add or subtract the values at each point where it makes sense. If the functions are given by formulas, you can just add or subtract the formulas (it doesn't matter whether you plug in values before or after).

Step-by-step explanation:

Lisa [10]2 years ago
4 0

Here's an example of adding two functions

f(x) = 5x^2+7x+10\\\\g(x) = 3x^2-2x+4\\\\f(x)+g(x) = (5x^2+7x+10)+(3x^2-2x+4)\\\\f(x)+g(x) = (5x^2+3x^2)+(7x-2x)+(10+4)\\\\f(x)+g(x) = 8x^2+5x+14\\\\

We basically add the expressions like normal. There are 3 pairs of like terms

  • 5x^2 \text{ and } 3x^2 which combine to 8x^2
  • 7x \text{ and } -2x which combine to 5x
  • 10 \text{ and } 4 which combine to 14

==========================================================

Now let's say we wanted to subtract those two functions.

f(x) = 5x^2+7x+10\\\\g(x) = 3x^2-2x+4\\\\f(x)-g(x) = (5x^2+7x+10)-(3x^2-2x+4)\\\\f(x)-g(x) = 5x^2+7x+10-3x^2+2x-4\\\\f(x)-g(x) = (5x^2-3x^2)+(7x+2x)+(10-4)\\\\f(x)-g(x) = 2x^2+9x+6\\\\

Notice in the fourth line, the negative distributes to each term inside the parenthesis. This is because we're subtracting off 3x^2 and also subtracting off -2x (i.e. adding 2x) and also subtracting off 4 all from f(x).

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