Find the domain of f(x)=(sqrt(x+2))/(x^2-16)

sqrt(x+2) has the domain 

 when  or 

so the domain is [2, 4) U (4, oo)

Find the excluded value(s) for the following expression : 4x/(x^2+x-6)

Rational expressions are defined whenever their denominators are real and non-zero, so...
x^2+x-6=(x+3)(x-2)=0
x=-3 or x=2

avoid {-3, 2}

Find the domain of f(x)= sqrt5+4x-x^2

the domain for any polynomial function is all real numbers

Find the domain

Find the domain of f(x) = 1/sqrt(|x|-7)

we require that  
this means that 
|x|-7>0
|x|>7 
so 
(-oo,-7) U (7,oo)

h(x)= abs(-2x) What are the domain and range? x=-3 What are the domain and range?

h(x) has domain (-oo,oo) and range [0,oo) 
x=-3 hs domain {-3} and range (-oo,oo)

Find the domain of f(y)=sqrt(81-y^2)

What is the domain of the function f(x)=-3?

all real numbers because no matter what x is f(x) is -3

find the domain and range of y=3/(2x-3)

 
has domain     



and range     

what is the domain using interval notation for :f(y)= y+9/y^2-9y

Assuming you mean to write 
 
then y can take on any value except 0 or 9 and so 
Domain: 
(-oo,0) U (0,9) U (9,oo) 


:)

the domain of the function f(x)=ln(2x+4) is?

Natural log is defined only for positive numbers so 
2x+4>0 
and so 

 
is the domain

find the domain of x^3-6x^2+15x+5

The domain for any polynomial is all real numbers.

how to find the domain of n(x)=x+3/4

The function n(x)=x+3/4 is a linear function (that has a defined, nonzero slope) and therefore its domain is all real numbers (and so is its range).


:)

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Give the domain and range of G. Write your answers using set notation

Suppose that the relation is defined as follows. {(5,5),(8,0),(6,-2),(-9,-8)} Give the domain and range of G. Write your answers using set notation

G={(5,5),(8,0),(6,-2),(-9,-8)}
The domain is the set of x-coordinates and the range is the set of y-coordinates:

dom(G)={5,8,6,-9}
ran(G)={5,0,-2,-8}

:)

Find the domain and range.

Find the domain and range.
R={( -4, -7), ( 12, 5), ( 11, -9), ( 11, -3)}


Solution:

The domain of a relation is the set of all first coordinates so we can write Dom R={-4, 12, 11}

The range of a relation is the set of all second coordinates so we can write Ran R={-7, 5, -9, -3}

Find the domain of the function