Question

Let f and g be functions from the positive real numbers to positive real numbers defined by f(x) = [2x]

g(x) = x².2 Calculate f o g and g o f.

Answer 1

The integral part or integer part of $x,$ often denoted $[x]$ is usually defined as the $\lfloor x\rfloor$ if $x$ is nonnegative, and $\lceil x\rceil$ otherwise.

$$f\circ g=[g]=[2x^2]=\lfloor 2x^2\rfloor, since \ 2x^2\geq0,x\in\R$$

$$g\circ f=(f)^2=([2x])^2$$