Answer:
A rational expression that has the nonpermissible values [tex]x = 0[/tex] and [tex]x = 17[/tex] is [tex]f(x) = \frac{4}{x\cdot (x-17)}[/tex].
Step-by-step explanation:
A rational expression has a nonpermissible value when for a given value of [tex]x[/tex], the denominator is equal to zero. In addition, we assume that both numerator and denominator are represented by polynomials, such that:
[tex]f(x) = \frac{p(x)}{q(x)}[/tex] (1)
Then, the factorized form of [tex]q(x)[/tex] must be:
[tex]q(x) = x\cdot (x-17)[/tex] (2)
If we know that [tex]p(x) = 4[/tex], then the rational expression is:
[tex]f(x) = \frac{4}{x\cdot (x-17)}[/tex] (3)
A rational expression that has the nonpermissible values [tex]x = 0[/tex] and [tex]x = 17[/tex] is [tex]f(x) = \frac{4}{x\cdot (x-17)}[/tex].
