eviant:

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

2 months ago
eviant:

@Falconmaster

2 months ago
Falconmaster:

me no smart

2 months ago
dude:

(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))

2 months ago
Falconmaster:

i dont do meth or math moth i do do tho moth memes e.e

2 months ago
eviant:

@ dude I meant g^-1

2 months ago
eviant:

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

2 months ago
mhchen:

g^-1 is an inverse function. Do you know how to find the inverse of 3x-4?

2 months ago
Study2Learn:

I believe the answer is -2.

2 months ago
eviant:

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

2 months ago
mhchen:

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

2 months ago
mhchen:

But the trick here is: \[g^{-1}(g(x)) = x\] so \[g^{-1}(g(-2)) = -2\]

2 months ago
eviant:

so, how is -2 the final answer?

2 months ago
Study2Learn:

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

2 months ago
eviant:

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

2 months ago
eviant:

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

2 months ago
eviant:

^^how is that related to -2?

2 months ago
mhchen:

That's just the inverse of g(x)

2 months ago
Study2Learn:

^

2 months ago
mhchen:

g^-1(x)

2 months ago
eviant:

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

2 months ago
mhchen:

Well actually. g^-1(x) = (x+4)/3 g(x) = 3x+4 g^-1(g(x)) = x so g^-1(g(-2)) = -2

2 months ago
mhchen:

Is it still confusing?

2 months ago
eviant:

I think I got it....

2 months ago
eviant:

@mhchen, how did you find the final answer

2 months ago
eviant:

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

2 months ago
mhchen:

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

2 months ago
eviant:

how do I do that?

2 months ago
mhchen:

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.

2 months ago
Study2Learn:

Good work.

2 months ago