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Basic Inverse Trigonometric Functions

Assume that ...

Question

Assume that $f (1) = 0$ and that for all integers m and n. $f (m + n) = f (n) + 3 (4 m n - 1)$ then f(19)=

A

213

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B

209

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C

194

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D

199

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Solution

The correct option is A 213
Given $f (m + n) = f (n) + 3 (4 m n - 1), f (1) = 0$
Put $n = 1 ⟹ f (m + 1) = f (1) + 3 (4 m - 1) = 12 m - 3$
Let $m = 18$
$⟹ f (18 + 1) = 12 \times 18 - 3 = 216 - 3 = 213$

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