Question

What if we have fractions, @rational

For example: f(x) = 12/4x+2. Find f(-1)

So, we're finding the inverse, too, yes? I would basically isolate x and do the same thing, correct?

Answer 1

Exactly ! but use proper parenthesis so that the expression is not ambiguous

Answer 2

y = 12/4x+2
y * 12 = 4x + 2
y * 12 - 2 = 4x
y * 12 -2/4 = x
y * 10/4 = x

Are we off to a good start?

Answer 3

12/4x+2

do you mean

\[\large \dfrac{12}{4x}+2\]

or

\[\large \dfrac{12}{4x+2}\]

or

\[\large \dfrac{12}{4}x+2\]

or what ?

Answer 4

b

Answer 5

i thought so, you should use parenthesis to group the bottom stuff :
f(x) = 12/(4x+2)

Answer 6

y = 12/(4x+2)

cross multiply :
4x+2 = 12/y

subtract 2 both sides :
4x = (12/y) - 2

divide 4 both sides :
x = (3/y) - 1/2

Answer 7

you need
f(-1) or \(f^{-1}\)
?

Answer 8

f(-1) is just 1 plugged in place of x

Answer 9

Yes, it's f(-1) not f^-1, but what does f^-1 mean?

Answer 10

@Compassionate if it is confusing, solve
\[\large \dfrac{12}{4x+2}=10\] and see the method

Answer 11

then solve
\[\large \dfrac{12}{4x+2}=\pi\]

Answer 12

Okay, so: x = (3/y) - 1/2


I understand how we got this, now we just need to plug in -1, right?

Answer 13

and finally solve
\[\large \dfrac{12}{4x+2}=y\] or if you prefer solve \[\large \dfrac{12}{4y+2}=x\]

Answer 14

\(f^{-1}\) is the inverse function of f

f(-1) is the value of f(x) when x =-1

Answer 15

\[f^{-1}(x)\] has nothing to do with the number \(-1\)
it means the inverse function

Answer 16

Okay, Satellite, If I do the last one, we have.

12/(4x+2) = y
12/y = 4x+2
10/y = 4x
(10/y)/4 = x

Answer 17

on the other hand, i see that you wrote find \(f(-1)\) which is a whole different story than find \(f^{-1}(x)\)

Answer 18

which is it?

Answer 19

It's f(-1), not hte inverse.

Answer 20

then don't find the inverse ! :P
just plug in x=-1 in f(x)

Answer 21

f(-1) = 12/ (-4+2) = ...

Answer 22

\[\large f(x)=\frac{12}{4x+2}\\
f(-1)=\frac{12}{4\times (-1)+2}\]

Answer 23

\(\large f(x)=\frac{12}{4x+2}\\
f(-1)=\frac{12}{4\times (-1)+2} \\
f(\heartsuit )=\frac{12}{4\times (\heartsuit )+2}\)

Answer 24

hey!

Answer 25

i patented \(f(\clubsuit)\)

Answer 26

lol, thats why i was careful not to use it :P

Answer 27

Okay, so...

f(x) = 12/(4x+2). Find f(-1)

y = 12/(4[-1]+ 2)
y = 12/(-4 + 2)
y = 12/-2
y = -6

Answer 28

\(\huge \checkmark\)

Answer 29

It's the idea of an inverse that throws me off. Could you explain a bit more in detail on this?

Answer 30

as sat said, inverse is altogether a different story!
f(-1) and \(f^{-1}\)

Answer 31

so, you want details about inverse or f(-1)
?

Answer 32

f^-1

Answer 33

\[f(x) = 7x - 13. Find f^{-1}(x).\]

For example

Answer 34

that is inverse function and has nothing to do with this question

Answer 35

I am aware, but I am asking for you to elaborate a little bit on an inverse and what it is. Would you prefer me to close and open a new question?

Answer 36

a function f and g are inverses of each other, iff
\(f(g(x)) =x , \\ and \\ g(f(x))=x\)

to get inverse function of y=f(x) , we replace x by y and y by x and then isolate x

this is essentially to make f(g(x)) =x

Answer 37

f(x) = 7x - 13. Find f^-1(x)

So I could say.
y = 7x - 13
y + 13 = 7x
(y + 13)/7 = x

And then reverse

(x + 13)/7 = y,

Right?

Answer 38

absolutely! :)

Answer 39

I'm really getting the hang of this (:

Answer 40

cool :)
find the inverse of 1/x :)

Answer 41

*dies*

Answer 42

1/x isn't an equation. How does one find the inverse.

Answer 43

ok then

f(x) =1/x

Answer 44

f(x) = 7x - 13. Find f(x) = 1/x

Uh. f(x) = 7(1/x) - 13? cx

Answer 45

no...i gave you another function....
forget that f(x) was 7x-13

Answer 46

ok,
g(x) =1/x
find
\(g^{-1}(x)\)

Answer 47

Uh. y = 1/x
y * 1 = x?

x * 1 = y

Answer 48

so whats xx ?

Answer 49

x***

Answer 50

g(x) =1/x

xx? No no. I solve for x. I replaced g(x) with y.

y = 1/x. I undid the division by multiplying

So y * 1 = x

Then I "inversed" them by swapping y and x.

Answer 51

ok, so whats your final answer for the inverse function ?

Answer 52

It's x * 1 = x

Answer 53

inverse function is a function
\(g^{-1}(x) =... ?\)
(in terms of x)

Answer 54

My brain has reached maximum capacity.

Answer 55

x=1/y
so
y=1/x
so
\(g^{-1}(x) = 1/x\)
an example of the function whose inverse is itself

Answer 56

This is too much. My brain wasn't built for this.