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Find g[f(x)] if f(x) =`sqrt(x^2 -2)and g(x) = x^2 + 2`

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Find g[f(x)] if f(x) =`sqrt(x^2 -2)and g(x) = x^2 + 2`

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To determine g( f(x) ), substitute x=f(x) in the function g(x).

`g(f(x))=x^2+2`

`g(f(x))=(f(x))^2+2`

Since `f(x)=sqrt(x^2-2)` , then

`g(f(x))=(sqrt(x^2-2))^2+2`

`g(f(x))=x^2-2+2`

`g(f(x))=x^2`

Hence, `g(f(x))=x^2 ` .

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