Question

The composition of functions is associative.

Answer 1

Define functions and verify to get the desired result.

Let $h\left(x\right)=x^3,g\left(x\right)=x^2$ and $f\left(x\right)=x$
Then, $\left[ho\right(gof\left)\right]\left(x\right)=h\left(g\right(f\left(x\right)\left)\right)$
$=h\left(g\right(x\left)\right)$
$=h\left(x^2\right)$
$=x^6\dots \left(1\right)$
Now, $\left[\right(hog\left)\text{of}\right]\left(x\right)=\left(hog\right)\left(f\right(x\left)\right)$
$=\left(hog\right)\left(x\right)$
$=h\left(g\right(x\left)\right)$
$=h\left(x^2\right)$
$=x^6\dots \left(2\right)$
Comparing equation $\left(1\right)$ and $\left(2\right)$, we get
$ho\left(gof\right)=\left(hog\right)$ of
Therefore, composition of functions is associative

Hence, the given statement is True.