Find Where Undefined/Discontinuous f(x)=(x+3)/(x^2+9)

Problem

ƒ(x)=(x+3)/(x2+9)

Solution

1. Identify the type of function. This is a rational function, which is undefined or discontinuous only where the denominator is equal to zero.

2. Set the denominator equal to zero to find potential points of discontinuity.

x2+9=0

3. Solve for x by subtracting 9 from both sides.

x2=−9

4. Analyze the result. In the set of real numbers, the square of any number is non-negative (x2≥0. Therefore, there is no real value of x such that x2=−9

5. Conclude that since the denominator is never zero for any real input, the function is defined and continuous for all real numbers.

Final Answer

Undefined/Discontinuous: None (Continuous for all real *x*)

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