Explanation
Step 1
Let
[tex]\begin{gathered} g(x)=x^2+1 \\ g(f(x))=x^2+4x+5 \end{gathered}[/tex]so,
A composite function is generally a function that is written inside another function. Composition of a function is done by substituting one function into another function
so, when evaluate f(x) into g(x) we got
[tex]\begin{gathered} g(x)=x^2+1 \\ g(f(x))=x^2+4x+5 \\ so \\ g(x)=x^2+1 \\ g(f(x))=(f(x))^2+1 \\ \text{hence} \\ (f(x))^2+1=x^2+4x+5 \end{gathered}[/tex]Step 2
solve for f(x)
[tex]\begin{gathered} (f(x))^2+1=x^2+4x+5 \\ \text{subtract 1 in both sides} \\ (f(x))^2+1-1=x^2+4x+5-1 \\ (f(x))^2=x^2+4x+4 \\ \text{factorize} \\ (f(x))^2=(x+2)^2 \\ \text{square root} \\ \sqrt{(f(x))^2}=\sqrt{(x+2)^2} \\ f(x)=(x+2) \end{gathered}[/tex]therefore, the answer is
[tex]f(x)=(x+2)[/tex]I hope this helps you
