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3. Suppose f(x) = x squared - 2x +3 and g(x) = x squared -3. Compute the composition f(g(x)) and simplify.

User Manie
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1 Answer

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The given functions are


\begin{gathered} f(x)=x^2-2x+3 \\ g(x)=x^2-3 \end{gathered}

The composition f(g(x)) refers to substituting the x-variables of f(x) for the function g(x).


f(g(x))=(x^2-3)^2-2(x^2-3)+3

Then, we solve the power and product. We solve the squared binomial using the following


(a-b)^2=a^2-2ab+b^2
\begin{gathered} f(g(x))=x^4-2\cdot x^2_{}\cdot3+9-2x^2+6+3 \\ f(g(x))=x^4-6x^2-2x^2+18 \\ f(g(x))=x^4-8x^2+18 \end{gathered}

Therefore, the composition is


f(g(x))=x^4-8x^2+18

User Fissio
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