Define the functions f(x) and g(x) import math

def f(x): return x3 + 5*x2 + x

def g(x): return 4**x

Given value of x

x_value = 5

Compute (f+g)(x), (f-g)(x), (fg)(x), and (f/g)(x)

f_plus_g = f(x_value) + g(x_value) f_minus_g = f(x_value) - g(x_value) f_times_g = f(x_value) * g(x_value) f_divided_by_g = f(x_value) / g(x_value)

Round to two decimal places

f_plus_g_rounded = round(f_plus_g, 2) f_minus_g_rounded = round(f_minus_g, 2) f_times_g_rounded = round(f_times_g, 2) f_divided_by_g_rounded = round(f_divided_by_g, 2)

f_plus_g_rounded, f_minus_g_rounded, f_times_g_rounded, f_divided_by_g_roundedHere are the evaluated expressions at $x = 5$:

• $(f + g)(5) = 1279$
• $(f - g)(5) = -769$
• $(fg)(5) = 261120$
• $\left( \frac{f}{g} \right)(5) \approx 0.25$

Would you like to explore further details or have any questions about these results?

Here are some related questions for you:

1. How would the values change if $x = 6$?
2. What happens if we calculate these expressions with different values for the functions $f(x)$ and $g(x)$?
3. Can we calculate the derivative of these functions $(f+g)(x)$ or $(fg)(x)$?
4. How would you evaluate these functions for complex numbers or negative values of $x$?
5. What is the significance of the quotient $\left( \frac{f}{g} \right)(x)$ being so small for $x = 5$?

Tip: When dealing with complex expressions, using a systematic approach like breaking down each function step-by-step helps avoid calculation errors.