How do you find (f o g)(x) if $g(x) = (x^2 -16)^(1/2)$ , $f(x) = (3 - x)^(1/2)$ ?

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Answer 1 · 2018-03-17T11:53:49

$(f@ g)(x)= sqrt(3- sqrt((x+4)(x-4)))$

$f(x) = (3-x)^(1/2)= sqrt(3-x)$

$g(x) = (x^2-16)^(1/2)=sqrt((x+4)(x-4))$

$(f@ g)(x)$ means $f(g(x))$

$:. (f@ g)(x)= f (sqrt((x+4)(x-4)))$ or

$(f@ g)(x)= sqrt(3- sqrt((x+4)(x-4)))$ [Ans]

How do you find (f o g)(x) if g(x) = (x^2 -16)^(1/2)g(x) = (x^2 -16)^(1/2), f(x) = (3 - x)^(1/2)f(x) = (3 - x)^(1/2)?