11th Grade Q1

Multiplying two functions is like finding the product of their outputs at the same input. Here's how you do it: To multiply $f(x)$ and $g(x)$, you combine their expressions as:

Example

1. Start with the functions: Write the two functions you want to multiply. For example:

1. Set up the multiplication: Substitute the expressions for $f(x)$ and $g(x)$:

1. Simplify: Expand the product using the distributive property:

Combine like terms:

1. Interpret the result: The new function $f\cdot g$ is the product of the two original functions. You can now evaluate it for any $x$. For example, if $x=1$, then:

Summary

• Write the product $(f\cdot g)(x)=f(x)\cdot g(x)$.
• Expand and simplify the expression using the distributive property.
• Use the result to evaluate the function for any input.