Math Problem Statement
f(x) = 2x^2 - 3x + 1, g(x) = f(2x) + 3, find g(x)
Solution
You provided two functions and are tasked with finding . Here’s the breakdown:
Given:
We need to substitute into the function .
Step 1: Find
Start with the given function , and substitute in place of :
Simplifying each term:
Step 2: Calculate
Now, substitute into the equation for :
Final Answer:
Would you like any further details or clarification?
Here are 5 related questions to deepen your understanding:
- How would the result change if ?
- Can you find the derivative of the function ?
- What would happen if were a cubic function instead of a quadratic one?
- How does changing the function from to affect ?
- Can you find the inverse of ?
Tip: When substituting variables, be careful with distributing powers and constants to ensure accuracy in each step.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Algebra
Functions
Substitution
Formulas
f(x) = 2x^2 - 3x + 1
g(x) = f(2x) + 3
Theorems
-
Suitable Grade Level
Grades 9-11