First slide

Properties of ITF

Question

If 6 $\sin^{- 1} (x^{2} - 6 x + 12) = 2 π$ , then the value of $x,$ is

Moderate

A

1
B

2
C

3
D

none of these

Solution

We have,
$x^{2} - 6 x + 12 = (x - 3)^{2} + 3 \geq 3$ for all $x$
$∴ \sin^{- 1} (x^{2} - 6 x + 12)$ does not exist.
Thus, there is no value of x satisfying the given equation.

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