# Revision history [back]

Hello, @Arnab! I suppose the following is the answer you're looking for. First define $f$:

f(x) = x^2 + 1


Now compose simply by writing:

f2(x) = f(f(x))
f3(x) = f(f(f(x)))


As you might guess, $f2$ is the composition $f\circ f$ with itself, while $f3$ is the composition $f\circ f\circ f$.

The same mechanism works for different functions. Let's define

f(x) = x^2 + 1
g(t) = t^3


Then you can write

fg(t) = f(g(t))
gf(x) = g(f(x))


The first one will give you $t^6+1$, while the second will give you $(x^2+1)^3$.

I hope this helps!

Hello, @Arnab! I suppose the following is the answer you're looking for. First define $f$:

f(x) = x^2 + 1


Now compose simply by writing:

f2(x) = f(f(x))
f3(x) = f(f(f(x)))


As you might guess, $f2$ is the composition $f\circ f$ ($f$ with itself, itself), while $f3$ is the composition $f\circ f\circ f$.f$(three times$f$). The same mechanism works for different functions. Let's define f(x) = x^2 + 1 g(t) = t^3  Then you can write fg(t) = f(g(t)) gf(x) = g(f(x))  The first one will give you$t^6+1$, while the second will give you$(x^2+1)^3\$.

I hope this helps!