Write down the equations of the asymptotes of the functions below \( g(x)=3 \tan (2 x) \quad \) where \( x \in\left[-90^{\circ} ; 90^{\circ}\right] \)

For the function g(x) = 3 tan(2x), we need to find the values of x for which the function is undefined. Recall that the tangent function is undefined when its argument is an odd multiple of 90° (because the cosine is zero at these angles). Step 1: Identify where tan(θ) is undefined. tan(θ) has vertical asymptotes when:   θ = 90° + k·180°  for any integer k. Step 2: Substitute 2x for θ. Since our function is tan(2x), set:   2x = 90° + k·180° Solve this for x:   x = (90° + k·180°) / 2   x = 45° + k·90° These are the equations for the vertical asymptotes in terms of x. Step 3: Pick the asymptotes that fall within the given domain x ∈ [–90°, 90°]. Let’s test several integer values for k: • For k = -1: x = 45° + (-1×90°) = 45° - 90° = -45° • For k = 0: x = 45° + 0 = 45° • For k = 1: x = 45° + 90° = 135° (This is outside the domain.) Thus, within the domain [–90°, 90°], the vertical asymptotes are at:   x = -45°  and  x = 45°. These are the equations of the asymptotes for the function g(x) = 3 tan(2x).