A graph of a function f is given below 15 Find the domain an

A graph of a function f is given below. 15 Find the domain and range of f. (Enter your answers using interval notation.) domairn range

Solution

1- From graph : Domain x values over which graph exists

0<= x <=6

interval notation [ 0 , 6 ]

Range : y vaues over which graph exist 3 <= y < =9

interval notation [ 3 , 9 ]

2- f(x) = x^2 + x +2 ; g(x) = x-3

a) (f +g)(x) = x^2 +x +2 +x -3 = x^2 +2x -1

b) ( f- g)(x) = x^2 +x +2 - x +3 = x^2 +5

c) (f o g)(x)

Plug x = g(x) in f(x)

(f o g)(x) = (x-3)^2 +( x-3) +2

= (x-3)( x-3 +1) +2 = (x-3)(x-2) +2

= x^2 - 5x +6 +2 =x^2 -5x +8

d) ( g o f)(x)

Pug x= f(x) in g(x)

( g o f)(x) = (x^2 +x +2) -3 = x^2 +x -1