Question

when looking at a rational function f of x equals the quantity x plus three times the quantity x minus two times the quantity x plus five all divided by the quantity x minus three times the quantity x plus two times the quantity x minus 5, charles and bobby have two different thoughts. charles says that the function is defined at x = –2, x = 3, and x = 5. bobby says that the function is undefined at those x values. who is correct? justify your reasoning.

Answer 1

$f(x)= \frac{(x+3)(x-2)(x+5)}{(x-3)(x+2)(x-5)}$ is undefined when the denominator is 0. i.e. x - 3 = 0 or x + 2 = 0 or x - 5 = 0 i.e. x = 3 or x = -2 or x = 5.
Hence, Bobby is right.