Given that y = 1 - \(\frac{2x}{4x - 3}\), find the value of x for which y is undefined
Answer Details
To find the value of x for which y is undefined, we need to look for values of x that make the denominator of the expression for y equal to zero, since division by zero is undefined.
The denominator of the expression for y is 4x - 3. Therefore, we need to find the value of x that makes 4x - 3 equal to zero.
Solving the equation 4x - 3 = 0, we get:
4x = 3
x = 3/4
Therefore, the value of x for which y is undefined is x = 3/4.
Explanation:
To understand why we need to look for values of x that make the denominator of the expression for y equal to zero, we need to remember that division by zero is undefined. When we divide a number by zero, there is no answer because it is impossible to divide any number into equal parts of zero size.
In the given expression for y, the denominator is 4x - 3. If we plug in x = 3/4, the denominator becomes:
4x - 3 = 4(3/4) - 3 = 3 - 3 = 0
This means that when x = 3/4, the denominator becomes zero, and therefore division by zero occurs, which makes the value of y undefined.
Hence, the value of x for which y is undefined is x = 3/4.