Let and . Then a value of is

Question

Let  and . Then a value of  is

Canvas Classes · Accepted Answer

🧠 Solve the Functional Equation First — Then Plug Into the Sine-Inverse

The custom binary operation . Constraint: .

Compute each side.

. Then .

Set equal: , so .

Let : , factoring as . So  (impossible since ) or .

Therefore , hence .

Compute the inverse-sine expression:

.

So .

🗺️ Working It Out

Decode the constraint.

.

Setting equal: , so .

Solve for : Let . Then . The non-negative root is .

So , .

Compute the bracket:

.

Final:

.

⚡ Two-Step Structure: Functiona

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