Solution
GivenIn this question, we are given that
• A function g, which is defined by \(g(x)=\frac{(6x-3)(x+4)}{(x-1)(x+2)(x-3)}\)
To findWe need to determine
• The values of x, for which g(x) is undefined
Approach and Working outAs g(x) is in the form A/B, the function g(x) will be undefined when the denominator B will become 0.
Here, the denominator is in the form of a product of three elements: (x – 1), (x + 2), and (x – 3)
If the product of these elements is 0, then at least one of these 3 elements must be equal to 0
• If (x – 1) = 0, then x = 1
• If (x + 2) = 0, then x = -2
• If (x – 3) = 0, then x = 3
Hence, x can be either 1 or -2 or 3.
Thus, option E is the correct answer.
Correct Answer: Option E _________________