Question 5 Given two functions \( f(x)=x^{6}-4 x^{4} \) and \( g(x)=x^{2} \), find and simplify the following: a) \( (f g)(x)=\square 99 \) pt \( 2 \leftrightarrows \) b) \( \left(\frac{f}{g}\right)(x)=\square \) Question Help: Video 1 Video 2 Written Example 1 D Post to forum

We are given the functions f(x) = x⁶ - 4x⁴ and g(x) = x². a) To find (fg)(x), multiply f(x) by g(x):   (fg)(x) = (x⁶ - 4x⁴) · x² = x⁶·x² - 4x⁴·x² = x⁸ - 4x⁶. b) To find (f/g)(x), divide f(x) by g(x):   (f/g)(x) = (x⁶ - 4x⁴) / x². We can simplify by dividing each term by x² (note: x ≠ 0):   x⁶ / x² = x⁴  and 4x⁴ / x² = 4x². Thus, (f/g)(x) = x⁴ - 4x², with the condition x ≠ 0 (because division by zero is undefined). Final Answers: a) (fg)(x) = x⁸ - 4x⁶ b) (f/g)(x) = x⁴ - 4x² (for x ≠ 0)