Practice problem
If f(x)=x2+1f(x)=x^2+1f(x)=x2+1, g(x)=1xg(x)= \dfrac{1}{x}g(x)=x1, and h(x)=x+3h(x)=x+3h(x)=x+3, find f(g(h(x)))f(g(h(x)))f(g(h(x)))
f(g(h(x)))=1x2+6x+10f(g(h(x)))=\dfrac{1}{x^2+6x+10}f(g(h(x)))=x2+6x+101
f(g(h(x)))=1x2+6x+9+1f(g(h(x)))=\dfrac{1}{x^2+6x+9}+1f(g(h(x)))=x2+6x+91+1
f(g(h(x)))=(1x+3+1)2f(g(h(x)))=\begin{pmatrix}\dfrac{1}{x+3}+1\end{pmatrix}^2f(g(h(x)))=(x+31+1)2
f(g(h(x)))=(x+3x)2+1f(g(h(x)))=\begin{pmatrix}\dfrac{x+3}{x}\end{pmatrix}^2+1f(g(h(x)))=(xx+3)2+1
Type a concept, like “slope” or “photosynthesis”.