Question

determine whether f(x0=5x+1/x and g(x)-x/5x+1 are inverses with steps y'all

Answer 1

@Falconmaster

Answer 2

i dont think so it does not look like it

Answer 3

have any steps i know it isn't but i have to show work

Answer 4

oh umm mathway might be able to help

Answer 5

https://www.mathway.com/BasicMath

Answer 6

i tried you have to pay for steps

Answer 7

if you have it slove it and show the steps

Answer 8

f(x)=square root 2x-6 find inverse

Answer 9

sorry thats all i can do i wiah i could help more

Answer 10

@Vocaloid

Answer 11

@Layla help?

Answer 12

hold on for 1 sec

Answer 13

gotta have steps

Answer 14

okay

Answer 15

I'm on my phone so this might be hard to explain but

You have to calculate f(g(x)) and g(f(x)) and if they both equal to x they are inverses

Answer 16

[ 5 [ x / [ 5x + 1] ] + 1 ] / [ x / [5x + 1] ] =
[ (5x + 5x + 1 ) / [ 5x + 1) ] / [x / [5x + 1] ] =
( [ 10x + 1] / x ] =
10 + 1/x
is this right

Answer 17

yes

Answer 18

next question give me a sec

Answer 19

find the inverse function for squre root 2x-6

Answer 20

Let y = sqrt(2x-6)

Switch y and x and then re-solve for y

Answer 21

To find the inverse interchange the variables and solve for y.
y=square root 2x-6
x=square root 2y-6
divide each side by 2
f^-1(x)=x^2/2 +3
i feel like i missed a step

Answer 22

Why are you dividing by 2?

Answer 23

6/2=3 right

Answer 24

If you have x = sqrt(2y-6) you should square both sides

Answer 25

oh ok

Answer 26

and the rest is right?

Answer 27

Right

The answer is correct but the steps are incomplete

Answer 28

f(x)=(x-2)^3+8
i have to find inverse and show that this is one to one?

Answer 29

Same process for finding the inverse

I actually forgot how to show one to one so I will look it up

Answer 30

lol i know how to graph it and determine but not algebraically

Answer 31

Ok to show one to one you have to show that

f^1(f(x)) = x

Answer 32

f^(-1) sorry

Answer 33

do i just multiply f and x?

Answer 34

You take the function f(x) and let it be your x value in the function f^-1

Answer 35

So you would replace x with (x-2)^3+8 in the inverse

Answer 36

To find the inverse interchange the variables and solve for y.
y=(x-2)^3+8
now what would i do and how would i square the other problem i got x=x^2 and that's about it

Answer 37

x = (y-2)^3 +8

Subtract 8 from both sides then take the cube root

Answer 38

Welcome to QC! ^_^

Answer 39

so -8=(y-2)=x

Answer 40

Not quite

cuberoot(x-8) = y - 2

Answer 41

so next do we cube it ? i guess

Answer 42

No just solve it for y

Answer 43

All you have to do is add 2 to both sides

Answer 44

2+cube root -8+x?

Answer 45

Don't change what's inside the root symbol just add 2 outside

Answer 46

y = cuberoot(x-8) + 2

Answer 47

ok so cube x-8 +2

Answer 48

Good just make sure to write the correct root symbol

Answer 49

mathway has the same answer in a different form

Answer 50

Yeah that's normal, you can write using a different form as long as it's the same function

Answer 51

now one to one part of it

Answer 52

@sillybilly123 are you free to take over? I have an exam coming up

Answer 53

You just need to show that f^-1(f(x)) = x

Answer 54

nah, mate!!

you've found the inverse. the OP now needs to go through the definition of a function.

i had a play with the original question, which was quite diffrent, on Desmos and the **inverse function** is a function if you slice and dice.

the one you've done looks good, IMVHO, and so should be OK. your exams are more important. go study!

Answer 55

i wass about to say didn't i technically prove that it's one-to-one