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Question

Number of ordered pair $open parentheses s close parentheses open parentheses a comma blank b close parentheses$ for each of which the equality $a open parentheses cos invisible function application x minus 1 close parentheses plus b to the power of 2 end exponent equals cos invisible function application open parentheses a x plus b to the power of 2 end exponent close parentheses minus 1$ holds true for all $x element of R$ are

1
2
3
4

The correct answer is: 2

Putting $x equals 0 blank rightwards double arrow b to the power of 2 end exponent equals cos invisible function application b to the power of 2 end exponent minus 1 rightwards double arrow cos invisible function application b to the power of 2 end exponent equals 1 plus b to the power of 2 end exponent rightwards double arrow b equals 0$
For $blank b equals 0 comma$ we have $blank a open parentheses cos invisible function application x minus 1 close parentheses equals cos invisible function application a x minus 1$
$rightwards double arrow 2 a sin to the power of 2 end exponent invisible function application fraction numerator x over denominator 2 end fraction equals 2 sin to the power of 2 end exponent invisible function application fraction numerator a x over denominator 2 end fraction$
$rightwards double arrow a equals 0$ or $blank a equals 1$
Hence, ordered pairs are $open parentheses a comma blank b close parentheses identical to open parentheses 0 comma blank 0 close parentheses$ or $blank open parentheses 1 comma blank 0 close parentheses$

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