Let be given by and let be given by

MATHEMATICS · Subjective · GCSE · Mathematics · Algebra · Algebra

Problem

Let

f:[0,\infty)\to[0,\infty)

be given by

f(x)=\sqrt{x}

and let

g:[0,\infty)\to[0,\infty)

be given by

g(x)=x^{2}

. (a) Calculate

(g\circ f)(x)

for an arbitrary

x\in[0,\infty)

. (b) Calculate

(f\circ g)(x)

for an arbitrary

x\in[0,\infty)

. (c) Evaluate the results of parts (a) and (b) specifically at

x=1,4

and

9

. (d) Using your work above, determine whether

f

and

g

are inverses of each other on

[0,\infty)

. Justify your answer clearly.