Question

If g(x) = 3x − 4, what is the value of g−1(g(−2))?

Answer 1

@Falconmaster

Answer 2

me no smart

Answer 3

(g(-2)) is the function of g when x is -2
Substitute -2

g-1 -- I am not sure if you meant g(-1)(g(-2))

Answer 4

i dont do meth or math

moth i do do tho


moth memes e.e

Answer 5

@ dude I meant g^-1

Answer 6

3(-2)-4=-2
Is -2 the answer?

Answer 7

g^-1 is an inverse function.

Do you know how to find the inverse of 3x-4?

Answer 8

I believe the answer is -2.

Answer 9

@mhchen how do you find the inverse of 3x-4?

Answer 10

S2L is correct.

So to find the inverse you basically get x by itself:

g(x) = 3x - 4
g(x) + 4 = 3x
(g(x) + 4) / 3 = x

Now switch x and g(x)

(x+4)/3 = g^-1(x)

That's the inverse

Answer 11

But the trick here is:

\[g^{-1}(g(x)) = x\]
so
\[g^{-1}(g(-2)) = -2\]

Answer 12

so, how is -2 the final answer?

Answer 13

Yea, to find the inverse, interchange the variables and solve for y.
f^-1 (x) = 4/3 + x/3

Answer 14

@ mhchen I don't understand how x+4/3 is related to -2

Answer 15

\[\frac{ x+4 }{ 3 }\]

Answer 16

^^how is that related to -2?

Answer 17

That's just the inverse of g(x)

Answer 18

^

Answer 19

g^-1(x)

Answer 20

so, the final answer is \[\frac{ 2 }{ 3 }\]

Answer 21

Well actually.

g^-1(x) = (x+4)/3
g(x) = 3x+4

g^-1(g(x)) = x

so

g^-1(g(-2)) = -2

Answer 22

Is it still confusing?

Answer 23

I think I got it....

Answer 24

@mhchen, how did you find the final answer

Answer 25

after finding the inverse of 3x-4, what did you do then?

Answer 26

I then plugged g(x) in for x

Since the question asked to find g^-1( g(x) )

That's plugging g(x) inside g^-1(x)

You don't even need to find the inverse. Just use this trick.

\[g^{-1}(g(x)) = x\]

Answer 27

how do I do that?

Answer 28

Okay so let me start over.

The question is:
\[g^{-1}(g(-2))\] right?

and

\[g(-2) = 3(-2) -4 = -10\]

right?

Then
\[ g^{-1}(-10) = \frac{(-10) + 4}{3} = -2\]

And that's the answer.

Answer 29

Good work.