Question

Find the domain and range of f(x)=(2x+3)/(x-5) using f(x) and the inverse of f(x).

Answer 1

domain: \[x=\mathbb{R}\]\[x \neq5\]

Answer 2

and whats thee range.

Answer 3

um. i don't think there's a limit on the range but i'm not entirely sure.

Answer 4

if there's a limit on x, there's a limit on y

Answer 5

So,
domain =\[(-\infty,5)\cup(5,\infty)\] and range =\[(-\infty,\infty)\]

Answer 6

There has to be a limit on y if there's a limit on x

Answer 7

you can't evaluate f(5)

Answer 8

no there doesn't. it just means that y isn't undefined

Answer 9

I'll find out what y can't equal. All I have to do is just find the inverse

Answer 10

since f(x) has an inverse, that proves that there's a limit on y

Answer 11

just look at the sine function, there's a limit on the range but not on the x

Answer 12

so what's thee range?

Answer 13

y cannot equal 2

Answer 14

liamarie, you're saying it backwards. With the sine function x has no limit. But what I said earlier is that if there is a limit on x, there's a limit on y. It doesn't work the other way around.

Answer 15

Can I ask how you got 2?

Answer 16

I found the inverse of f(x)

Answer 17

f^-1(x) = (5x+3)/(x-2)

Answer 18

hm. i stand corrected.

Answer 19

wouldnt it be, (5x-3)/(x+2)

Answer 20

No. I don't know how you got that. But no

Answer 21

ahah okay, thanks.

Answer 22

We can prove that f(x) cannot equal 2 by setting f(x) = 2 and solving for x

Answer 23

Do that and see what happens.