Function

[inner pumice]

I have no idea how to do this, i even looked up the text book but my brain cant process things , kindly teach me from scratch.

[thick ether]

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[swift hazel]

are you good at rearranging formulae

you can think of a function as a human eating food and the inverse function being a food eating a human 💀

so basically if i have a function f

the inverse function f^-1

will map back the values

so if f(3) = 5

then f^-1(5) = 3

its the opposite of what the original function is doing

but ofc the domain and range resrictions still apply to the inverse function

as you can see here i have two functions f(x) and g(x), where g(x) is the inverse of f

f(0) = 3

and g(3) = 0

its like taking a number and multiplying it by 3 (the original function) and then dividing it by 3 (the inverse function)

@inner pumice did my explanation make sense

[inner pumice]

my slow brain is trying to process it

[swift hazel]

ok lmk if you have any questions

[inner pumice]

im having trouble on a) do i need to do f-^(x)→2x+4...sorry im bad at understanding math really

im struggling to understand the concept

[coral lintel]

To algebraically find the inverse function, you can use a four-step method. For starters, what exactly do you know about inverse functions?

[inner pumice]

reversing a process?

[night parrot]

Kocher

[woven raven]

That should help clear things up.

[night parrot]

Kocher

[woven raven]

The latter represents the inverse functions.

[woven raven]

Sure. But what do they satisfy?

i.e., what properties?

[coral lintel]

It can be a process. The easiest method I can think of is strictly following the definition of what an "inverse function" is, and simply plotting the points based on what you know from the original graph.

If we look at inverse functions in the most simplest way, we can say: if f(a) = b, then f^(-1)(b) = (a). I'm sure the textbook you have would provide the formal definition for this, but if you'd like to solve this with the four-step method, feel free to let me know and I'll outline the process for you.

[inner pumice]

suree

[inner pumice]

to be honest , i don't think i really understand what an inverse function actually means

[coral lintel]

Not a problem. If you'd like, you can forward us how your textbook defines an inverse function and let us know what is confusing you about the diction.

Firstly, I'll assume that you're only working with inverses that are also functions; so the first step (using the Horizontal Line Test) may be omitted depending on what the question is asking you.

Here are the rest of the steps from a former textbook of mine:
Step 2: in the equation for f(x), replace f(x) with y
Step 3: interchange the roles of x and y, and solve for y
Step 4: Replace y with f-1(x) in the new equation

[woven raven]

@inner pumice If this makes a bit more sense.

In the context of the problem, what would the mapping of $f^{-1}$ be represented by?

[night parrot]

Kocher

[sand ridge]

yeah since f(x)=2x-4 let x=y and vice versa to get x=2y-4 then solve for y

[inner pumice]

guys is the answer y=x+4/2

[coral lintel]

Not quite. Please show us how you arrived to that answer.

[inner pumice]

y=2x-4
x=2y-4
x+4=2y
x+4/2=y

f^-1(x)=x+4/2 @coral lintel

[woven raven]

Where are you parentheses?

[inner pumice]

thank you for correcting me , is f^-1(x)=(x+4)/2 the final answer?

[woven raven]

Yep.

[inner pumice]

i dont understand how to do this

[coral lintel]

That equation can be further simplified, but I suppose it’s up to personal or instructor preference.

Simply graph both the original and inverse functions onto the plane they give you. Are you familiar with the steps needed to graph linear functions?

[inner pumice]

no , im not familiar and very clueless

[coral lintel]

Okay. Simplify your inverse equation, if you find it necessary to understand Slope-Intercept Form. Utilize the photo to help you graph both equations.

[inner pumice]

i don't know how to use this I'm sorry

[sand ridge]

its not necessary

you just graph inverse and regular function which you already identified

[inner pumice]

i have no idea how to draw it.

[swift hazel]

firstly, you have the function written out

then

you plug in values of x

and find values for u

y

[inner pumice]

like x1 , y1?

[woven raven]

You can use the given slope and/or y-intercepts.

[royal wagon]

@inner pumice

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Hello cieloshio, this is a friendly reminder that your help request has been inactive for more than 24 hours. If you no longer need assistance, please consider closing the thread using the +close command. This thread will be automatically closed in 3 days if it remains inactive.

[royal wagon]

@woven raven @swift hazel @sand ridge @coral lintel The user still needs help with this help request.

[woven raven]

@inner pumice What do you need help with?

[inner pumice]

i still cant figure it out how to sketch em💔

[swift hazel]

@inner pumice

do you know how to plot points on a graph

[inner pumice]

no..

[swift hazel]

do you know how to read points from a graph

[inner pumice]

like (0,0) (2,2)?

[swift hazel]

yeah