https://file.aiquickdraw.com/mathbot/file/172642601511994grhghe.jpg

The given function is:

\[
f(x+3) = 2x^2 - 3x + 1
\]

We are asked to find \( f(x+1) \).

### Step-by-step solution:

1. Substitute \( x+1 \) into the expression for \( f(x+3) \). Notice that \( x+3 = (x+1) + 2 \), so we can rewrite the function by replacing \( x \) with \( x-2 \) (because \( (x+1) - 2 = x-1 \)).

\[
f(x+1) = 2(x-2)^2 - 3(x-2) + 1
\]

2. Now, expand the terms:

\[
f(x+1) = 2[(x-2)^2] - 3(x-2) + 1
\]
\[
(x-2)^2 = x^2 - 4x + 4
\]
\[
f(x+1) = 2(x^2 - 4x + 4) - 3(x - 2) + 1
\]

3. Simplify the expression:

\[
f(x+1) = 2x^2 - 8x + 8 - 3x + 6 + 1
\]
\[
f(x+1) = 2x^2 - 11x + 15
\]

Thus, the required function is:

\[
f(x+1) = 2x^2 - 11x + 15
\]

Would you like a more detailed breakdown, or do you have any further questions?

Here are 5 related questions you might find useful:
1. How would you solve \( f(x+2) \) using the same method?
2. Can you apply the same substitution technique to a different type of function?
3. What happens if you try to find \( f(x) \) from \( f(x+3) \)?
4. How do you expand \( (x-2)^2 \) systematically in algebra?
5. Can this method be applied to other function transformations, such as shifts and stretches?

**Tip:** When substituting into a function, always adjust the variable properly by analyzing the new terms relative to the original equation.

If f(x + 3) = 2x^2 - 3x + 1, find f(x+1).

Learn how to find f(x+1) by applying substitution and expansion to the equation f(x+3) = 2x^2 - 3x + 1. This problem covers key algebraic concepts like function transformation and polynomial expansion. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation