Question

HELP!
f(x)=eˆ(x/2)-2 ; Df=R
find the zero points to the function
find asymptotes to the function

Answer 1

To find the zeros of a function f(x) you are trying to find the values x for which f(x)=0

Answer 2

so given:
\[f(x)=e^{\frac{x}{2}}-2\]
We want to find the values for x such that:
\[f(x)=e^{\frac{x}{2}}-2=0\]

Answer 3

Btw what is Df=R supposed to mean?

Answer 4

Anyways, we can find the zero by doing the following:
\[e^{\frac{x}{2}}-2=0 \\ e^{\frac{x}{2}}=2 \]
Take the natural log of both sides:
\[ \ln(e^{\frac{x}{2}})=\ln(2) \\ \frac{x}{2} \ln(e) = \ln(2) \]
The natural log of e is 1 therefore:
\[ \frac{x}{2} = \ln(2) \\ x = 2 \ln(2) \]

Answer 5

Oh thank you so much. the Df suppos to me the definition amount

Answer 6

huh? i dont understand

Answer 7

Your welcome... please give me a medal if you feel i have earned it. Do you still need help with the asymptote part?

Answer 8

Thank you again :D

Answer 9

can you draw the graph to the function and calculate the area bounded by graph to the function and line x=4 ?

Answer 10

wolframalpha.com is a very hand site to check answers and graph simple functions (pretty much any function you would encounter in early HS or College level algebra, trig, or calculus)

Answer 11

:) thanx

Answer 12

are there bounds on where to calculate the area from?

Answer 13

no its just the real numbers

Answer 14

well then the area is -infinity since the function f(x) has an asymptote of -2 (the value the function approaches but NEVER actually reaches)

Answer 15

so if you go from x=-infinity to x=4 then the area is -infinity because of all the negative area to the left of the vertical (y) axis

Answer 16

unless you are looking to calculate the area from the ZERO of the function to x=4 or from x=0 to x=4, which is it?

Answer 17

well i think its from x=0

Answer 18

i mean either is possible.... but the answer REALLY depends on the left bound so it is very important for that to be correct

Answer 19

Btw do you know do you know why the asymptote of this function is -2?

Answer 20

Keep in mind if you dont know its ok just say so... no judgement here :D

Answer 21

Are you still there?

Answer 22

Sorry, I am back now. Well i am not sure why its -2 :P

Answer 23

Ok well any well behaved function of the form:
\[f(x)=e^{g(x)} \] will NEVER equal zero.... If you want to convince your self of this fact try and solve:
\[f(x)=e^{g(x)} =0\]
Applying the same process as before, taking the natural log of both sides:
\[ \ln(e^{g(x)})=g(x) =\ln(0)\] which is impossible because ln(0) is undefined.... plot the logarithm function and you will see it has a vertical asymptote at zero

Answer 24

As a simple example just plot the function f(x)=e^x using the wolfram alpha site I gave you... you will see it has a horizontal asymptote at x=0... i.e. it NEVER touches the horizontal axis

Answer 25

So the function you gave me was of the form:
\[ f(x)=e^{g(x)} -2 \]
Which is just the exponential function vertically shifted down by two units.... hence the horizontal asymptote moves down by two units also. If you plot this function using that website you will confirm this.

Answer 26

And by "down by two units" i mean the horizontal asymptote for the exponential function is usually at zero... so moving down by two gives us a horizontal asymptote at y=-2

Answer 27

Does this make sense?

Answer 28

Yeh, thanks I really appreciate it :)

Answer 29

No problem :D and use that site as a handy calculator... it is really quite powerful... anyways for the second question about the area if you wouldnt mind could you please close this question and open another for that one and I will join you. Also make sure you post the correct domain for x as I mentioned the answer really depends on the domain.

Answer 30

ok, I will but I have to translate the problem from norwegian to the english first :)

Answer 31

Oh hahaha nice I didnt realize... well your English is very good. Please pardon mine as my typing isnt the best.

Answer 32

Yes it is the best :)

Answer 33

calculating the area bounded to f, the x-axis and the line x = 4 if it clear so I can post it as another problem

Answer 34

Yes please post it as another problem.