# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-6/6

Exercises: Try Out - Set 6: Real exam simulation to sharpen your skills and build confidence. - Question 6

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## Exercise 6

### Question

export const metadata = {
  title: "Question 6",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/23/2025",
};

Given functions <InlineMath math="f(x) = 2x - 3" /> and <InlineMath math="(g \circ f)(x) = 4x^2 - 12x + 10" />. The value of <InlineMath math="g(1)" /> is ....


### Choices

- [ ] $$1$$
- [x] $$2$$
- [ ] $$3$$
- [ ] $$4$$
- [ ] $$5$$

### Answer & Explanation

export const metadata = {
  title: "Solution for Question 6",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/23/2025",
};

We are given the function <InlineMath math="f(x) = 2x - 3" /> and the composite function <InlineMath math="(g \circ f)(x) = 4x^2 - 12x + 10" />. We are asked to find the value of <InlineMath math="g(1)" />.

The definition of a composite function is <InlineMath math="(g \circ f)(x) = g(f(x))" />. Let <InlineMath math="u = f(x) = 2x - 3" />. We rearrange this equation to express <InlineMath math="x" /> in terms of <InlineMath math="u" />:

<MathContainer>
  <BlockMath math="2x = u + 3" />
  <BlockMath math="x = \frac{u + 3}{2}" />
</MathContainer>

Substitute <InlineMath math="x" /> into the equation <InlineMath math="(g \circ f)(x)" />:

<MathContainer>
  <BlockMath math="g(u) = 4\left(\frac{u + 3}{2}\right)^2 - 12\left(\frac{u + 3}{2}\right) + 10" />
  <BlockMath math="g(u) = 4\left(\frac{u^2 + 6u + 9}{4}\right) - 6(u + 3) + 10" />
  <BlockMath math="g(u) = (u^2 + 6u + 9) - (6u + 18) + 10" />
  <BlockMath math="g(u) = u^2 + 6u - 6u + 9 - 18 + 10" />
  <BlockMath math="g(u) = u^2 + 1" />
</MathContainer>

Thus, we have <InlineMath math="g(x) = x^2 + 1" />.

Then the value of <InlineMath math="g(1)" /> is:

<MathContainer>
  <BlockMath math="g(1) = 1^2 + 1 = 1 + 1 = 2" />
</MathContainer>

So, the value of <InlineMath math="g(1)" /> is <InlineMath math="2" />.


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