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Find the domain of the fo f(u)=(u+14)/(5+(3)/(u+9))

User Cpuguru
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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.

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User Jay Sun
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