Final answer:
To find the domain of the function f(u)=(u+14)/(5+(3)/(u+9)), set the denominator equal to zero and solve for u. The domain is all real numbers except -48/5.
Step-by-step explanation:
To find the domain of the function f(u) = (u + 14) / (5 + 3 / (u + 9)), we need to identify the values of u that make the function undefined. This occurs when there is a division by zero. So, we set the denominator equal to zero and solve for u:
5 + 3 / (u + 9) = 0
We can multiply both sides of the equation by (u + 9) to eliminate the fraction. This gives us:
5(u + 9) + 3 = 0
Now, let's solve for u:
5u + 45 + 3 = 0
5u + 48 = 0
5u = -48
u = -48/5
Therefore, the domain of the function is all real numbers except -48/5.
Learn more about Domain of a function