Define the functions f(x)=x^ 2 +1

MATHEMATICS · Multi-part · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Define the functions

f(x)=x^{2}+1,\qquad g(x)=4x-3,

where

x\in\mathbb R

. Answer the following questions regarding the composite

(g\circ f)(x)

. (i) Calculate

(g\circ f)(2)

. (ii) Verify whether

(g\circ f)(-2)

is defined and, if so, find its value. (iii) For a general real number

k

, write a single algebraic expression for

(g\circ f)(k)

. Simplify your result.