Let and . If , and , then the value of is:

Question

Let  and . If , and , then the value of  is:

Canvas Classes · Accepted Answer

🧠 Reading the Question — Two Functional Equations, Two Tricks

This is a hybrid problem. You have two functional equations to solve:

1.  — pair  and . Substitute  for the second equation, then solve as a  system to get  explicitly.

2.  — here  is a constant (not a function evaluated dynamically). Solve for  in terms of that constant, then plug  to fix the constant.

After getting  and  explicitly, integrate each on  and combine.

🗺️ Working It Out

Find . From the given: . Substitute : .

Tw

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