The function g is given by g(x)=f(2x). find x such that g(x)=0

The function \( g(x) \) is given by:

\[
g(x) = f(2x)
\]

To find \( x \) such that \( g(x) = 0 \), we need to solve:

\[
g(x) = 0
\]

Substitute \( g(x) = f(2x) \) into the equation:

\[
f(2x) = 0
\]

Now, let’s introduce a substitution: let \( u = 2x \), which simplifies the equation to:

\[
f(u) = 0
\]

The value \( u \) is the solution to \( f(u) = 0 \). Once you find \( u \), you can solve for \( x \) by using the relation \( u = 2x \), which gives:

\[
x = \frac{u}{2}
\]

So, the \( x \)-value you're looking for is half of the value of \( u \) that makes \( f(u) = 0 \).

### Do you have the function \( f(u) \), or any more details about it?

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Here are five relative questions to expand on this:

1. What is the explicit form of the function \( f(x) \)?
2. Are there specific constraints on \( x \) for the function \( g(x) \)?
3. Can \( f(x) \) have more than one solution for \( f(u) = 0 \)?
4. Is the function \( f(x) \) continuous or differentiable?
5. Would you like to see the graphical representation of \( f(x) \) if given?

**Tip:** Always check if \( f(x) \) has multiple zeros to ensure you find all possible \( x \)-values for \( g(x) = 0 \).

The function g is given by g(x) = f(2x). Find x such that g(x) = 0.

Learn how to solve for x in the function g(x) = f(2x) when g(x) = 0. This solution involves function composition, substitution, and solving equations. Ideal for high school students in Grades 10-12, this step-by-step guide simplifies the process.

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