$If f (x) = x^{2} - 1, and g (x) = x - 2,$ $then find a, if g o f (a) = 1.$

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Solution

The correct option is D 2
$g o f (a) = g {f (a)}$
$Given, f (x) = x^{2} - 1, and g (x) = x - 2$
$∴ g {f (a)} = g {a^{2} - 1}$
$= (a^{2} - 1) - 2 = a^{2} - 3$
$Given, g o f (a) = 1$
$∴ a^{2} - 3 = 1 \Rightarrow a^{2} = 4 \Rightarrow a = \pm 2$

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