Question
If $f(x)=x^2-1, g(x)=x-2$ find $a$, if $g \circ f(a)=1$
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Answer
$f(x)=x^2-1, g(x)=x-2$
Given $\operatorname{gof}(a)=1$
$g \circ f(x)=g(f(x))$
$=g\left(x^2-1\right)=x^2-1-2$
$=x^2-3$
$g \circ f(a) \Rightarrow a^2-3=1$
$a^2=1+3$
$=4$
$a= \pm 2$
Given $\operatorname{gof}(a)=1$
$g \circ f(x)=g(f(x))$
$=g\left(x^2-1\right)=x^2-1-2$
$=x^2-3$
$g \circ f(a) \Rightarrow a^2-3=1$
$a^2=1+3$
$=4$
$a= \pm 2$
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