Consider the functions , (with ) and

MATHEMATICS · Subjective · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Consider the functions

f(x)=x^{2}+1

g(x)=\dfrac{1}{x-2}

(with

x\neq2

) and

h(x)=|x|

. (i) Determine

(g\circ f)(x)

. (ii) Using the result of part (i), evaluate

(h\circ g\circ f)(-1)

. (iii) List all real numbers

x

for which

(h\circ g\circ f)(x)

is defined, giving reasons for any restrictions.