Question

function rule of gx if fx is fx^2

Answer 1

If \( f(x) = x^2 \), and you want to define a new function \( g(x) \) based on \( f(x) \), you can specify \( g(x) \) in several ways depending on the "rule" you want to apply. Here are a few examples:

1. **Direct Succession**: If you want \( g(x) = f(x + 1) \):
\[
g(x) = (x + 1)^2
\]

2. **Linear Transformation**: If you want \( g(x) = f(kx) \) for some constant \( k \):
\[
g(x) = (kx)^2 = k^2 x^2
\]

3. **Composition**: If you want \( g(x) = f(f(x)) \):
\[
g(x) = (x^2)^2 = x^4
\]

4. **Addition of a Constant**: If you want \( g(x) = f(x) + c \) for a constant \( c \):
\[
g(x) = x^2 + c
\]

5. **Scaling or Stretching**: If \( g(x) = k f(x) \) for some constant \( k \):
\[
g(x) = k x^2
\]

If you have a specific transformation or relation in mind for \( g \) relative to \( f \), please specify, and I can provide further details or examples!