Question

find the natural domain of
f(z)=√2z+3

Answer 1

domain = z values that satisfy the equation and do not result in an imaginary number

range = f(z) values for given z values.

Answer 2

so how to calculate z?

Answer 3

we have\[f(z)=\sqrt{2z+3}\]i'd say u evaluate the real domain of the function and then see what natural numbers are in it :)

Answer 4

just note that under radical cant be negative :)

Answer 5

mukushla i cant work it

Answer 6

see we have 2z+3 under the radical right? :) so we must have\[2z+3\ge0\]which gives\[2z\ge-3\]divide by 2\[z\ge-\frac{3}{2}\]so the real domain of the function is all numbers greater than or equal to -3/2

Answer 7

there is a problem with my net...i cant use the drawing tool...sorry :( but i think u can get it from here :) what are the natural numbers greater than -3/2 ?

Answer 8

why divided by?is it bcos of the square rooy?

Answer 9

no...its a simple inequality..think of it as an equality

Answer 10

i mean divided by 2

Answer 11

u want to solve for z and so u most isolate z in the left side of inequality so u must divide it by 2 :)

Answer 12

i got it

Answer 13

but became more difficult,cos i only know the root formular method,and here is not a general equation