Question

can someone help me understand and find the domain and range of f(x) = sec 2x.

Im not really familiar with domain and range at all so you can explain like what they are and how im supposed to find them

Answer 1

Are you allowed to use a graphing calculator?

Answer 2

^

Answer 3

Cause that answer depends on what I'm about to teach you lol

Answer 4

Yes lol

Answer 5

looking at a graph first is not a bad way to do it

Answer 6

Okay... I put it into desmos. What do I exactly do now?

Answer 7

maybe look at the graph?

for all inputs [values of "x"], you are getting something defined out of that "function",... , apart from the bits when sec(x) = 1/cos(x) = 1/0

so your domain has to exclude the singularities?

Answer 8

do you know what a function is defined as?

you can glue these ideas of input/output ---- domain/range by know what that means.

https://www.mathsisfun.com/sets/function.html

Answer 9

Yes I obviously looked at the graph.

I think I see what you mean. Is the domain going to infinity or no?

Answer 10

Gradually but there are domain restrictions because the graph is not continuous.

Answer 11

\(\checkmark\)

Answer 12

Like exactly what kind of restrictions? how can I tell that?

Answer 13

Put the horse before the cart

If \(sec(x)\) goes off into \(\infty\) for certain values of \(x\), then those values that do so are excluded from the definition of \(\sec(x)\) as a function

Answer 14

so it's Domain is limited

Answer 15

um

Answer 16

to which number does \(\sec(\pi/2)\) map to?

Answer 17

so is \(\pi/2\) within the domain of the function \(f(x) = \sec(x)\)?

Answer 18

Isn't it undefined and doesn't map to any number or no?

Answer 19

yes, if a "plausible" function maps \(f(x_o) \to \infty\) then there is a problem with this "function" at \(x = x_o\), a singularity.

So we must exclude the various \(x_o\)'s from the Domain

Once we do, the range bit is easy

Answer 20

Ok i see and how do we exclude?

Answer 21

this is stuff i copied for sec(x), so adjust for sec(2x) <-- doubled-frequency

Answer 22

Im sorry I have to go. Thanks for helping, or at least trying to help. I might have to find someone else later that can like explain it a lot better. Thanks anyways.

Answer 23

Trust me, when the penny drops, this is the explanation that you will remember :)

Happy hunting !!

Answer 24

Sorry its not.... i just started learning domain and range because im in 9th grade. Your explanation is just too complex for someone that just started learning this.