Questions: Find all values (x=a) where the function is discontinuous. [f(x)=-3x/(7x-2)(2-4x)] (a=2/7, 1/2)

Solution Steps

To find the values of \( x = a \) where the function \( f(x) = \frac{-3x}{(7x-2)(2-4x)} \) is discontinuous, we need to identify the points where the denominator is zero, as these points will make the function undefined.

1. Set the denominator equal to zero: \((7x - 2)(2 - 4x) = 0\).
2. Solve for \( x \) in each factor.

To find the points where the function \( f(x) = \frac{-3x}{(7x-2)(2-4x)} \) is discontinuous, we need to determine where the denominator is zero. The denominator is given by:

\[ (7x - 2)(2 - 4x) \]

Set the denominator equal to zero and solve for \( x \):

\[ (7x - 2)(2 - 4x) = 0 \]

This gives us two equations to solve:

1. \( 7x - 2 = 0 \)
2. \( 2 - 4x = 0 \)

Solving these equations:

1. \( 7x - 2 = 0 \implies x = \frac{2}{7} \)
2. \( 2 - 4x = 0 \implies x = \frac{1}{2} \)

Final Answer