The question asks which function composition can result in the expression $3 - 6x$, given that $f(x) = 2x - 1$ and $g(x) = 2 - 3x$.

Solution:

1. Composition of Functions:

   • The notation $f \circ g$ or $f(g(x))$ means to substitute $g(x)$ into $f(x)$.
   • Similarly, $g \circ f$ or $g(f(x))$ means substituting $f(x)$ into $g(x)$.

2. Check $f(g(x))$:

   • We know $g(x) = 2 - 3x$.
   • Substituting $g(x)$ into $f(x)$, we get: $f(g(x)) = 2(2 - 3x) - 1 = 4 - 6x - 1 = 3 - 6x$ So, $f(g(x)) = 3 - 6x$.

   This matches the expression we are looking for.

Conclusion:

The correct composition is $f \circ g$, which is option E.

Would you like any further details on function composition? Here are some related questions you might find helpful:

1. What are the properties of function compositions?
2. How can you reverse a function composition?
3. What happens when you compose a function with its inverse?
4. How do you prove two functions are inverses?
5. What are the applications of function composition in calculus?

Tip: When composing functions, make sure to substitute the entire second function wherever the variable appears in the first function.