Question

The following function is one-to-one. Find its inverse. Find the domain and range of f and f^-1 and Please show all of your work.
f(x) = 8+x/x The following function is one-to-one. Find its inverse. Find the domain and range of f and f^-1 and Please show all of your work.
f(x) = 8+x/x @Mathematics

Answer 1

sorry disregard that

Answer 2

so you have y=(8+x)/(x) correct?

Answer 3

yes

Answer 4

To find the inverse, switch x and y and solve for the new y.

Answer 5

ok i got that part....but now its the domain and range of f and f^-1

Answer 6

Easiest way is by using a graphing calculator, do you have one?

Answer 7

yes. What do I put into though? lol

Answer 8

first you try to graph the original function y=(8+x)/(x)
and you do have a Ti calculator right?

Answer 9

yes i have a Ti84 plus

Answer 10

okay so once you graph that function go to 2nd GRAPH

Answer 11

You will notice that there is going to be some ERROR signs on it, in this case it has one error sign right?

Answer 12

well im putting in the original function and it tells me that there is an error in dim. Im going to y= then graph. What am I doing wrong?

Answer 13

Deselect Plot1, Plot2, or Plot3 if any of them are enabled.

Answer 14

Im not sure how to do that.

Answer 15

wait i figured out that part

Answer 16

on the y= tab there where you plug in the equation there is on the top where it says Plot1 Plot2 and Plot3 so if any of them are darkened you can just go up and click enter to deselect

Answer 17

ok so the graph shows to go across the x-axis at -9, is that correct?!

Answer 18

no, are you sure you have (8+x)/(x) plugged in just exactly how I wrote it?

Answer 19

ohhh- haha- no i left off the parenthesis. y=8/x-1 ??

Answer 20

but then how would i write the answer for the domain and range of f and f^-1?

Answer 21

okay so you have f graphed right?

Answer 22

yes

Answer 23

now look at your graph

Answer 24

ok

Answer 25

Now it should look like this, does it?

Answer 26

yes it does

Answer 27

okay so for domain you are looking at the x axis. So you determine where the graph starts and ends on whenever it is x. So as you can see this graph has two parts.

Answer 28

when going to the left and one going to the right

Answer 29

Now lets look at the one in the left side, in quadrant 3.

Answer 30

ok

Answer 31

so you are reading from left to right, where does the graph begin?

Answer 32

for the first part?

Answer 33

-7 ?

Answer 34

Look at the first part, it is coming from the negative direction