Question

The function r is given by r(x)=x-3/x 5. What are all solutions to r(x)>0?

A) x < -3 or x > 0
B) x < -3 or x > 3
C) x < 0 and x > 3
D) x < -3 and x > 0

Answer 1

The function r(x) = (x - 3)/x^5. To find the solutions to r(x) > 0, we need to determine the values of x that make the function positive. The function r(x) is positive when x < -3 or x > 0.

So option (D) is the correct answer.

Step-by-step explanation:

The function r(x) is given by r(x) = (x - 3)/x5. To find the solutions to r(x) > 0, we need to determine the values of x that make the function positive. Since we have a rational function, we need to consider the sign of the numerator and denominator.

For the sign of the numerator, we look at the expression (x - 3). This expression is positive if x > 3, and negative if x < 3.

For the sign of the denominator, we consider the variable x as a factor. Since x is in the denominator, the function will be positive if x > 0, and negative if x < 0.

Combining the signs of the numerator and denominator, we find that the function r(x) is positive when x < -3 or x > 0. Therefore, the correct answer is A) x < -3 and x > 0.