# What is g[f(x)] of f(x)= and g(x)= `x^2 + 2` ? I am at the step of multiplying the square roots and am not sure how to finish it from there. g( ) = ( ) () + 2 ` `

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### 2 Answers

Given g(x)=x^2+2. But the expresion for f(x) is not given.

Now g[f(x)]={(f(x))^2}+2.

Now suppose that f(x)=(x+1).

Then g[f(x)]={(x+1)^2}+2

={x^2+2x+1}+2

=x^2+2x+3.

`f(x)= (x^2+2)^2+2=x^4+4x^2+4+2=x^4+4x^2+6`