Find f^{-1}(a) for f(x)=x^3-1, a=7; f(x)=x^3+2x-1, a=2; f(x)=cs2x, a=1 on [0,]

[davidsocal]

Please help solve this Calculus problem. Thank you.

For problems 1-3, find the (f^-1)(a) for each function.

1. f(x)=x³-1, a=7

2. f(x)=x³+2x-1, a=2

3. f(x)=cs2x, a=1 on [0,]

 

[mmm4444bot]

For problems 1-3, find … (f^-1)(a) for each function.

1. f(x)=x³-1, a=7

2. f(x)=x³+2x-1, a=2

3. f(x)=cs2x, a=1 on [0,

]

Is that the way #3 appears in your assignment? Either way, there are errors.

I could guess that 'cs2x' means one of the following:

csc(2)·x
csc(2·x)
cos(2)·x
cos(2·x)

I would also need to guess what interval [0, ] is supposed to be, as the right endpoint is missing.

Please double-check your typing, and read the forum guidelines.

PS: These are precalculus exercises having to do with inverse functions. :cool:

---

Where did you get stuck, on the first exercise?

Do you understand this notation: f^-1(x) ?

If you do not, then do you understand this notation: f(x) ?

If you understand f(x), then do you know how to solve f(x)=7 for x?

Please respond to these questions, and we can go from there.

 

[stapel]

Please help solve this [algebra] problem.

We'll be glad to help! But first, we'll need to see what you've tried (and, thus, where you're getting stuck).

For problems 1-3, find the (f^-1)(a) for each function.

Did the instructions really say this? Or were the instructions perhaps more along the lines of "For each function, evaluate the inverse f ^-1 at the given value of a."

1. f(x) = x³ - 1, a = 7

Where are you stuck in the process? You renamed "f(x)" as "y", solved for "x=", swapped the variables, and renamed the new "y" as "f-inverse". Then you plugged in "7" for "x", and... then what?

2. f(x) = x³ + 2x - 1, a = 2

This one is more difficult, due to the form of the function. But you can still use the definition of "inverse" to get the necessary value:

By definition, the value of b necessary to get f (b) = a corresponds to the value of a necessary to get f ^-1(a) = b. So what value of b gives f (b) = a?

3. f(x) = cs2x, a = 1 on [0,https://www.freemathhelp.com/forum/image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAkAAAAfCAMAAAACwBekAAAAAXNSR0IArs4c6QAAAGNQTFRFAAAAAAAAAABVACtVACuAAFWqKwAAKwBVK1WAK1WqK4DUVQAAVQArVQBVVYDUVarUVar/gCsAgCsrgFUrgNT/qlUAqlUrqv//1IAr1IBV1NSq1P///6pV/9SA/9TU// q///Uwleq6wAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAeElEQVQoU41P2Q6AIAybihdeqIioKPz/V7qB OSDTZY03dUCfMDNiUcOm9QcTO5nlISFE7HdaltJzLDjLFdi2DFs7wHOQmBVx9fd/1r4j/i/cqkiyciVGzkWiw506g0idNRsI4LipuEhyiejlJGYOmQG25CR9woN3XvEBY8PTsrJAAAAAElFTkSuQmCC

When you reply with your work on questions (1) and (2), please include a corrected statement of question (3). Thank you!

 

[mmm4444bot]

[#3] is more difficult, due to the form of the function. But you can still use the definition of "inverse" to get the necessary value:

By definition, the value of b necessary to get f (b) = a corresponds to the value of a necessary to get f ^-1(a) = b. So what value of b gives f (b) = a?

I had been thinking of this approach for each of the exercises. I don't read the exercise as requiring actual definitions for the inverse functions; I would report just the requested outputs, based on an understanding of the inverse-function concept. (Maybe the class has not yet covered finding inverse functions.) :cool: