Question

g(x)=6+x+2e^x , find g^-1(8)

Answer 1

that means to find the inverse of g(8)

Answer 2

I understand that i need to find the inverse, i just don't know what I need to do with the "e"

Answer 3

err...im not sure about that..here let @Hero help you

Answer 4

thank you

Answer 5

everything is moved to the bottom.

5^-1 = 1/5

1/[6 + 8 + 2e^8]

what math are you taking?

Answer 6

Calculus I

Answer 7

@myfacewhen that only goes for numbers....but when it says \(g^{-1}\) its not the same as \({1\over g}\)

Answer 8

If I help, I'm just going to present solution steps. I'm not exactly interested in "teaching" at this point in time. I think @smoothmath might be the guy if you want step by step "guidance".

Answer 9

Better just go ahead, Hero. I'm unfortunately blanking on how to explain this.

Answer 10

If i see the answer, I can probably work the problem backwards to figure out where I'm getting stuck.

Answer 11

Try alpha if you just need the answer. Type "inverse function of"

Answer 12

lol brain fart yea sorry bout that

y = 6 + x + 2e^x

ln e^x = x

swap x for y

x = 6 + y + 2e^y

solve for y

I can actually solve it if you need me to sorry it took so long I had some private business to attend to.

Answer 13

I usually can solve for y but the e is what is throwing me off

Answer 14

e is a constant

Answer 15

treat it like you would treat \(a\) or \(x\) or \(\pi\)

Answer 16

I believe the e has to do with the exponential and logarithmic functions that we are working on in class. I think I cancel out the e with natural log but I'm not getting the correct answer

Answer 17

this problem can be easily solved by inspection

Answer 18

You can't replace y with 8

Answer 19

However, you can do this:
y = 6 + 8 + 2e^8

Then solve for y

Once you have the point, you can reflect it over the axis y = x to get the inverse

Answer 20

thank you.

Answer 21

\(g(x)=6+x+2e^x\)

notice \(g(0)=6+0+2e^0=6+2=8\)

therefore \(0=g^{-1}(8)\)