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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!