Question

What is the domain and range of f(x)?

Answer 1

wjat the finction?

Answer 2

\[f(x)=\frac{ 1 }{ \sqrt{2x-4} }\]

Answer 3

so 2y-4 cannot be <0

Answer 4

so 2x-4 cannot be <0
x>=2

Answer 5

Since it is in a fraction, it can't even be 0 right?

Answer 6

x>2?

Answer 7

yeah cannot be 0 too

Answer 8

yeah x>2

Answer 9

range would be?

Answer 10

no there is no limitations for range i think

Answer 11

@perl

Answer 12

would it also be y>0? as long as the denominator is not a 0, range>0?

Answer 13

hmm let me think let me grath best way

Answer 14

its suppose to be greater than 0
bec you can't have negative number under root

Answer 15

wait domain is (2, infinite), (x>2)
range {0, infinite), (y>=0)

Answer 16

here is right solution

Answer 17

how can the range ever be 0?

Answer 18

if x can't be 0?

Answer 19

sometimes

Answer 20

i get that the domain is x>2

not sure how range is x>=0

Answer 21

(2, infinite), (x>2)
range {0, infinite), (y>=0)

Answer 22

can you explain when y=0?

Answer 23

@Directrix

Answer 24

Y has to be positive because the numerator 1 is positive and the denominator has to be positive. So, y >0 but that may need some fine tuning. Let me think.

Answer 25

Y cannot be 0

Answer 26

ohh well when you graph this you can understand it better

Answer 27

so y>0
x>2

Answer 28

now see that kinda graph its almost near the x-axis but never gonna touch it

Answer 29

that's right

Answer 30

The graph is asymptotic to x = 2 so the range does increase without bound but not in a left to right way.

Answer 31

As x gets smaller and smaller, approaching 2, the value of the function sky rockets, increases without bound.

As x gets larger and larger, increasing without bound, the denominator gets larger and larger, increasing without bound. The numerator is stuck on 1 with an ever increasing denominator and approaches zero (x -axis) as a limit.

The x-axis is a horizontal asymptote.

Answer 32

Domain: x > 2 where x is real.

Range: 0 < y < oo where y is rea.

Answer 33

That is what I am thinking and why I'm thinking it.

Answer 34

oo coool :D

Answer 35

Looks good.

Answer 36

\[\infty =oo\]

Answer 37

0.0

Domains are not so bad but ranges are tricky.