Question

help me to answer this question.. given f(x)=5/2-x for x<2. find f inverse and its domain..

Answer 1

Let's replace f(x) with y....
\[\large y = \frac52-x\]is this correct?

Answer 2

yes.. but i don't know their domain...

Answer 3

can u help me find the domain?

Answer 4

after a few more steps it will become apparent

you want the inverse of this equation right? take @terenzreignz equation...and switch the x's and y's

Answer 5

can u show me? bcoz it have range for x<2.. so i'm not sure..

Answer 6

More on that later, for now, just switch the x and y, and show me what you got.

Answer 7

y=5/2-x

Answer 8

exactly.....since the inverse...is the same a the original equation...we can conclude this has no inverse correct?

Answer 9

Excuse me? The inverse of this function is not the original equation... ;)

Answer 10

oops....lol wow such a rookie mistake...forgive my last post

Answer 11

go back to finding the inverse...we have

x = 5/2 - y correct? solve for y again

Answer 12

Or it is... I'm not really sure :D

Answer 13

turns out it is... forgive MY last posts :D

Answer 14

Just seemed too good to be true.

Answer 15

wait really?

Answer 16

Yeah.. inverse of a-x is also a-x, for any constant a.
a-(a-x) = x

Answer 17

x = 5/2 - y
2x = 5 - 2y
-2y = 2x - 5
y = -x + 5/2

ahh looky there lol

Answer 18

Okay, @sha0403
To get the inverse of a function, switch x and y, and attempt to express y as purely an expression of x.

Answer 19

Step by step method courtesy of @johnweldon1993

Answer 20

lol, yeah sorry for the "spoonfeeding"...but I had to confirm with myself

Answer 21

but okay...since that is the inverse (original equation)

we want to find it's domain correct?

Answer 22

but, what the function of x<2 in the question? given?

Answer 23

Yes :) okay, back to
\[\huge f(x)=\frac52-x\]
And its domain is all x < 2
right?

Answer 24

yes

Answer 25

Now, if we consider its inverse (which, either annoyingly or conveniently, is itself)
we get
\[\huge f^{-1}(x)=\frac52-x\]
What do we know about inverses and the domain of the original function?

Answer 26

The range of the inverse must be the domain of the original function, right?

Answer 27

right...so can u explain the domain of the function in more specific, i'm not really understand it

Answer 28

The domain of a function f is all values of x for which f(x) has a value.
Take for instance
\[\huge g(x)=\frac1x\]
Its domain is all real numbers EXCEPT 0, since g does not have a value at g(0)

Answer 29

and for x<2? what the function of that? just ignore it or what?

Answer 30

No. This is what you call restricting the domain. If left without the x<2
Then we have
\[\huge f(x)=\frac52-x\]and its domain is all real numbers because, well, let's face it, no matter what real number you have for x, the function will be defined.

But the domain CAN be restricted to a smaller set. In this case, the domain could have been all real numbers, but instead, the domain is RESTRICTED to x<2
or
\[\large x\in(-\infty,2)\]

Answer 31

thank u very much.. i get it now..=)

Answer 32

So... how about the inverse of the function? That the range of the inverse of the function is the domain of the original function?

Answer 33

i not sure,,

Answer 34

Okay :)
Let y = f(x)
that is to say, y is a function of x.
The domain of f(x) is the set of all PERMISSIBLE values of x
The range of f(x) is the set of all POSSIBLE values of y, given that x comes from the domain.

An example...
\[\huge y =h(x)=|x|\]
the absolute value function... any real number can be evaluated under h (the absolute value)
so its domain is...
\[\huge dom \ h =\mathbb{R}\]

Answer 35

for the domain,, why the 2 is include? while the given x<2?

Answer 36

2 is not included :)

Answer 37

ok2 tq sir..

Answer 38

Now, the range of h... h is the absolute value, so it can only ever churn out non-negative numbers so...
\[\huge ran \ h = [0,\infty)\]

Answer 39

Back to your question...
\[\huge f^{-1}(x)=\frac52-x\]

Answer 40

We're asked for the domain, and we're given the domain of the original function, f(x) which is x < 2, right?

Answer 41

oh yes..SO?

Answer 42

Well, the range of the inverse is the domain of the original function, is that clear to you now? :)

Answer 43

so the domain for inverse function is negative infinity to 2?

Answer 44

No... that is the domain for the original function :)
The RANGE for the inverse function is negative infinity to 2. You following me so far? Don't worry, we're almost done ;)

Answer 45

i ask u how to find the domain of inverse function right? or have misunderstanding at there?

Answer 46

We are getting there. Just tell me if you understand everything so far.