Practice problem
Let f(x)=x3+3xf(x)=x^3+3xf(x)=x3+3x and g(x)=xg(x)=\sqrt xg(x)=x, find f(g(x))f(g(x))f(g(x)) and g(f(x))g(f(x))g(f(x)).
f(g(x))=(x)3+3(x)f(g(x))= (\sqrt x)^3+3(\sqrt x)f(g(x))=(x)3+3(x)
f(g(x))=x+3(x)f(g(x))= x+3(\sqrt x)f(g(x))=x+3(x)
f(g(x))=(x)3+(x)f(g(x))= (\sqrt x)^3+(\sqrt x)f(g(x))=(x)3+(x)
g(f(x))=x3/2⋅(3x)g(f(x))= x^{3/2}\cdot\sqrt{(3x)}g(f(x))=x3/2⋅(3x)
g(f(x))=x3/2+(3x)g(f(x))= x^{3/2}+\sqrt{(3x)}g(f(x))=x3/2+(3x)
g(f(x))=(x3+3x)g(f(x))= \sqrt{(x^3+3x)}g(f(x))=(x3+3x)
Type a concept, like “slope” or “photosynthesis”.