# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-5/19

Exercises: Try Out - Set 5: Real exam simulation to sharpen your skills and build confidence. - Question 19

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## Exercise 19

### Question

export const metadata = {
  title: "Question 19",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/23/2025",
};

Given <InlineMath math="f(x) = 2x - 3" />, <InlineMath math="g(x) = x^2 + 4x - 1" />, and <InlineMath math="(g \circ f)(x) = ax^2 + bx + c" />, then the value of <InlineMath math="a + b + c =" />


### Choices

- [ ] $$4$$
- [ ] $$3$$
- [ ] $$0$$
- [ ] $$-3$$
- [x] $$-4$$

### Answer & Explanation

export const metadata = {
  title: "Answer to Question 19",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/23/2025",
};

We are given the functions <InlineMath math="f(x) = 2x - 3" /> and <InlineMath math="g(x) = x^2 + 4x - 1" />. We need to find the value of <InlineMath math="a + b + c" /> from the composite function <InlineMath math="(g \circ f)(x) = ax^2 + bx + c" />.

First, let's determine the composite function <InlineMath math="(g \circ f)(x)" />:

<MathContainer>
  <BlockMath math="(g \circ f)(x) = g(f(x))" />
  <BlockMath math="= g(2x - 3)" />
  <BlockMath math="= (2x - 3)^2 + 4(2x - 3) - 1" />
</MathContainer>

Expand the squared term and the product:

<MathContainer>
  <BlockMath math="= (4x^2 - 12x + 9) + (8x - 12) - 1" />
</MathContainer>

Combine like terms:

<MathContainer>
  <BlockMath math="= 4x^2 - 12x + 8x + 9 - 12 - 1" />
  <BlockMath math="= 4x^2 - 4x - 4" />
</MathContainer>

From the form <InlineMath math="ax^2 + bx + c" />, we obtain:

<MathContainer>
  <BlockMath math="a = 4, \quad b = -4, \quad c = -4" />
</MathContainer>

So the value of <InlineMath math="a + b + c" /> is:

<MathContainer>
  <BlockMath math="a + b + c = 4 + (-4) + (-4)" />
  <BlockMath math="= 4 - 4 - 4" />
  <BlockMath math="= -4" />
</MathContainer>

Thus, the value of <InlineMath math="a + b + c = -4" />.


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