# Nakafa Framework: LLM

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

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

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## Exercise 5

### Question

export const metadata = {
  title: "Problem 5",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/23/2025",
};

If <InlineMath math="f(x) = x^2 + 4x - 5" /> and <InlineMath math="g(x) = 2x - 1" />, then <InlineMath math="(g \circ f)(x)" /> is ...


### Choices

- [x] $$2x^2 + 8x - 11$$
- [ ] $$2x^2 + 8x - 6$$
- [ ] $$2x^2 + 8x - 9$$
- [ ] $$2x^2 + 4x - 6$$
- [ ] $$2x^2 + 4x - 9$$

### Answer & Explanation

export const metadata = {
  title: "Solution to Problem 5",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/23/2025",
};

We want to find the composite function <InlineMath math="(g \circ f)(x)" />.

#### Understanding Function Composition

The composite function <InlineMath math="(g \circ f)(x)" /> is defined as:

<MathContainer>
  <BlockMath math="(g \circ f)(x) = g(f(x))" />
</MathContainer>

This means we will substitute the entire function <InlineMath math="f(x)" /> into the variable <InlineMath math="x" /> in the function <InlineMath math="g(x)" />.

#### Function Substitution

Given:
- <InlineMath math="f(x) = x^2 + 4x - 5" />
- <InlineMath math="g(x) = 2x - 1" />

We substitute <InlineMath math="f(x)" /> into <InlineMath math="g(x)" />:

<MathContainer>
  <BlockMath math="(g \circ f)(x) = g(x^2 + 4x - 5)" />
</MathContainer>

Since <InlineMath math="g(x) = 2x - 1" />, we replace every <InlineMath math="x" /> in <InlineMath math="g(x)" /> with <InlineMath math="(x^2 + 4x - 5)" />:

<MathContainer>
  <BlockMath math="(g \circ f)(x) = 2(x^2 + 4x - 5) - 1" />
</MathContainer>

#### Simplifying the Result

Now we distribute the multiplication and simplify:

<MathContainer>
  <BlockMath math="(g \circ f)(x) = (2 \cdot x^2) + (2 \cdot 4x) - (2 \cdot 5) - 1" />
  <BlockMath math="(g \circ f)(x) = 2x^2 + 8x - 10 - 1" />
  <BlockMath math="(g \circ f)(x) = 2x^2 + 8x - 11" />
</MathContainer>

#### Conclusion

Thus, the composite function is <InlineMath math="2x^2 + 8x - 11" />.


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