**Problem Statement:**Determine the big-theta (Θ) estimate for the function below. Show all relevant working.\[ f(x) = (3x^3 + 8x^2 - 7) \log(12x^7 + 6x^3 + 9x + 1) \]**Explanation:**To find the big-theta estimate, focus on the highest degree terms in both the polynomial and the logarithmic function, which dominate the behavior as \( x \to \infty \).1. **Polynomial Analysis:** - The highest degree term in the polynomial part \( 3x^3 + 8x^2 - 7 \) is \( 3x^3 \).2. **Logarithmic Analysis:** - The highest degree term in the logarithmic part \( \log(12x^7 + 6x^3 + 9x + 1) \) is \( \log(x^7) \) because the term \( 12x^7 \) dominates as \( x \to \infty \). - Using the logarithmic property, \(\log(ax^b) = \log(a) + b\log(x)\), we get \(\log(12x^7) \approx 7\log(x)\).3. **Combine Results:** - The function simplifies to: \( f(x) \approx 3x^3 \cdot 7\log(x) = 21x^3 \log(x) \).4. **Big-Theta Estimate:** - Hence, the big-theta estimate is \( \Theta(x^3 \log(x)) \). This means that as \( x \to \infty \), \( f(x) \) grows at a rate proportional to \( x^3 \log(x) \).

The complexity of an algorithm is expressed in theta notation. It limits a function from both the…

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›) Determine the big-theta estimate for the function below. Show all relevant working f(x) = (3x³ + 8x² — 7)log(12x7 + 6x³ + 9x + 1).