Question

determine whether 8x+1 and 4x+1 are non inverse or inverse?

Answer 1

May I help?

Answer 2

yes

Answer 3

With my pleasure!

which one do you want to start to get the other one?

Answer 4

it doesnt matter

Answer 5

You choose one!

Answer 6

f(X)=5x+1/x

Answer 7

Great!

Do you know how to get the inverse of a function?

Answer 8

no

Answer 9

im kind of confused

Answer 10

No problem at all!
Step by step, it will be easy In Sha' Allah


To get the inverse of any function f(x) [ just make sure that it passes the horizontal line test] follow the steps:
- Solve for x, i.e separate x in one side and the other terms in the other side, included f(x).
- Swap x and f(x).
- The result is the inverse of the original function \(f^{-1}(x)\).

try these!

Answer 11

im still kind of confused of how to find the f(x)=5x+1/x for inverse functions

Answer 12

Let's do it together!
agree?

Answer 13

yup

Answer 14

Great!

\[\LARGE f(x)=\frac{ 5x+1 }{ x }\]
Cross multiply:
\[\LARGE x*f(x)=5x+1\]
Make all x-terms in one side:
\[\LARGE x*f(x)-5x=1\]
Take x as a common factor:
\[\LARGE x[f(x)-5]=1\]
Solve for x now:
\[\LARGE x=\frac{ 1 }{ f(x)-5 }\]

Swap x and f(x):
\[\LARGE f^{-1}=\frac{ 1 }{ x-5 }\]

This is the inverse of f(x)!

Answer 15

@billyjean
Do you follow?

Answer 16

yes

Answer 17

what about for g(x)=x/5x+1 im kind of confused for that one

Answer 18

The same idea of the same procedure0!

Can you do it!

Answer 19

sorry im really confused on this question

Answer 20

i really need some help

Answer 21

So Where are you stuck?

Answer 22

for the inverse of x/5x+1 I got x/5x-1

Answer 23

Not quite correct!

Let's represent it as follows:

\[\LARGE\color{SeaGreen} {g(x)=\frac{x}{5x+1}}\]
Cross multiply:
\[\LARGE\color{SeaGreen} {g(x)*[5x+1]=x}\]
Distribute g(x):
\[\LARGE\color{SeaGreen} {5x*g(x)+g(x)=x}\]
Gather all x-terms in one side:
\[\LARGE\color{SeaGreen} {5x*g(x)-x=-g(x)}\]
Take x as a common factor:
\[\LARGE\color{SeaGreen} {x[5*g(x)-1]=-g(x)}\]
Solve for x:
\[\LARGE\color{SeaGreen} {x=\frac{ -g(x) }{ 5*g(x)-1 }}\]
or
\[\LARGE\color{SeaGreen} {x=\frac{ g(x) }{ 1-5*g(x)}}\]
Swap x and g(x):
\[\LARGE\color{DarkGreen } {g^{-1}(x)=\frac{ x }{ 1-5x}}\]


\[\large\underline{\color{MediumBlue }{ Are ~you~ persuaded~?}}\]

Answer 24

@billyjean Do you follow?

Answer 25

yes

Answer 26

I am happy to hear that.

Answer 27

any difficulties?

Answer 28

no thank you so much

Answer 29

Don't mention it!
Any Help... Any Time...
That is with my pleasure!

Answer 30

Any more questions?

Answer 31

no

Answer 32

I will not be late for any help.

Answer 33

In general \(\color{black}{\displaystyle f }\) and \(\color{black}{\displaystyle g }\) are inverses of each other, iff \(\color{black}{\displaystyle f[g(x)]=g[f(x)]=x }\).

Answer 34

Alternatively, you can try to find \(\color{black}{\displaystyle f^{-1}(x)}\) or \(\color{black}{\displaystyle g^{-1}(x)}\) , and if it turns out that \(\color{black}{\displaystyle f^{-1}(x)\ne g(x)}\) or \(\color{black}{\displaystyle g^{-1}(x)\ne f(x)}\), then, they are not inverses.

Answer 35

So, by this second approach, all you have to do is to find the inverse function of either \(f\) or \(g\).