Given the functions f(x)=2x+3, -5 x 4

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

Problem

Given the functions

f(x)=2x+3,\quad -5\le x\le4,\\ g(x)=x^{2},\quad x\ge -3,

consider the set

R=\{(x,y)\mid y=f(x)=g(x)\}.

(i) Determine the intersection of the domains of

f

and

g

. (ii) Solve the equation

f(x)=g(x)

within this intersection and hence list all elements of

R

. (iii) Find the range of

f

-5\le x\le4

and the range of

g

x\ge -3

separately. (iv) Using your answer to part (iii), explain why the range of

R

is a finite set and state this set explicitly.