11th Grade Q1

Adding two functions is like combining their outputs at the same input. Here's how you do it:
To add $f(x)$ and $g(x)$, you combine their expressions. Write:

Example

1. Start with the functions: Write the two functions you want to add. For example, suppose you have:

and

1. Add them together: Substitute the expressions for $f(x)$ and $g(x)$

1. Simplify: Combine like terms

1. Interpret the result: The new function $f+g$ is a combination of the two original functions. You can now evaluate it for any $x$. For example:If $x=1$, then:

Summary

To add functions:

• Add their outputs.
• Simplify the combined expression.
• Use the result to find values for any input.

Given the functions $f(x)$ and $g(x)$, calculate the value of their sum for the given $x$.

Generate exercises of the form:

"

"

The answer should have the form (f+g)(x_0) = . Both f and g must be on separate lines, and use math blocks. Add no additional text.

where a_0, a_1, a_2, b_0, b_1, b_2 and x_0 are different integers. The coefficients can take values from -5 to 5. If the coefficient is 0 remove the term. If the coefficient is 1 do not write the 1. x_0 can take values from -20 to 20.