Question

HELP MEEEE
How do you add and subtract functions?

Answer 1

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`

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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).

Answer 2

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).

Explanation: