Solving Inverse Shminverse Homework

[srfriggen]

Homework Statement

If f(x)= x^3 +4x + 6,

a.) show f(x) is one to one.

b) Find inverse f(10)... f^-1(10) (hard to write type on a computer)

c) Find f^-1(10)'

Homework Equations

f^-1(x)' = 1/[f'(x)*f^-1(10)]

The Attempt at a Solution

a.) a function is monotonic when it is either always increasing or always decreasing. You can check by looking at the derivative, f(x)' = 3x^2 + 4. This Function is one to one because it is monotonic (always increasing).

b.) I simply cannot figure this out. I am pretty sure our professor does NOT want us to try to find a direct equation for f^-1(x). I believe she wants us to use the method she calls "inspection", to look at the problem carefully and figure out a y value, then f^-1(x) = y, so I can find f(10). pretty lost.

c.) See above... though I know the equation is f^-1(x)' = 1/[f'(x)*f^-1(10)]

 

[tiny-tim]

Hi srfriggen!

(try using the X² tag just above the Reply box )

If f(x)= x^3 +4x + 6,

a.) show f(x) is one to one.

b) Find inverse f(10)... f^-1(10) (hard to write type on a computer)
…
b.) I simply cannot figure this out. I am pretty sure our professor does NOT want us to try to find a direct equation for f^-1(x). I believe she wants us to use the method she calls "inspection", to look at the problem carefully and figure out a y value, then f^-1(x) = y, so I can find f(10). pretty lost.

Yes, part a) told you f(x) is increasing, and you can immediately see that f(0) = 6 and f(1) = 11, so f^-1(10) must be between 0 and 1 …

now narrow it down further. ​

 

[srfriggen]

Hi srfriggen!

(try using the X² tag just above the Reply box )


Yes, part a) told you f(x) is increasing, and you can immediately see that f(0) = 6 and f(1) = 11, so f^-1(10) must be between 0 and 1 …

now narrow it down further. ​

That helps a little but doesn't really get to an answer. I have a feeling she meant to write 3x instead of 4x. That would make things a lot more elegant.

 

[Dick]

That helps a little but doesn't really get to an answer. I have a feeling she meant to write 3x instead of 4x. That would make things a lot more elegant.

She may also have meant f^(-1)(-10) instead. That would make more sense as well.

 

[srfriggen]

True, -10 would work nicely.

ok, I've been going batty trying to figure this one out. It was on a small pop quiz last night and she said it shouldn't have taken us more than a minute to do that problem...

so am I nuts and terrible at calc or does it seem like she made a mistake? cause I don't see an easy solution to this problem at all.

 

[Svensken]

What about 0?

(x-10)^1/2=f^-1(x)

or am i completely wrong

 

[srfriggen]

What about 0?

(x-10)^1/2=f^-1(x)

or am i completely wrong

The question asks what is f^-1(10). You ask if zero works...

No, because if f^-1(10)=0, then f(0) would have to equal 10, and f(0) is 0^3+4(0)+6, or 6.

 

[srfriggen]

Thank you all for replying. turns out my teacher did make a mistake. should have been 11, not 10.