Write x less than 6 in interval notation 7 infinite in inequ

Write x less than 6 in interval notation [-7, infinite) in inequality notation What is the domain for the following functions? f(x) = 2/x+1 g(x) = squareroot x - 3 h(x) = 3x^2 + x

Solution

8) a ) x < 6

Interval notation ( - infinity , 2 )

b) [ -7 , infinity)

Inequality notation: x<= -7

9) a) f(x) = 2/(x+1)

Domain: All execpt x=-1 when denominator is zero.

( - inf , 1) U ( 1, inf)

a) g(x) = sqrt(x-3)

Condition : (x- 3) > = 0

x> = 3

Domain : [ 3, infinity)

c) h(x) = 3x^2 +x

A polynomial exist at all real x

So,Domain : ( -infinty , +infinity)