Inverse function

[Octo]

Hi could someone help with this please. I got 0.83 for the first question but when I put the numbers in my attempt at the 2nd part it doesn't produce the answer of 3? Any help is much appreciated thanks

 

[Dr.Peterson]

Write out more steps, and check the details. You have one sign error.

Also, when you check your answer using the number you found (which was an excellent thing to do), don't use the rounded answer they asked for; use a more accurate value to avoid rounding errors: 0.8333333, or the entire value stored in your calculator.

Now, when I use the calculated value in your inverse, I get t = -3, which makes the sign error obvious. When I use 0.83, I get -0.92, which is very, very different. Clearly this equation is highly sensitive, and rounding to 2 decimal places is not a good idea!

 

[Octo]

Fantastic thank you so much this has been messing with my head for weeks! I thought the rounding would cause a deviation to the answer but didn't think it would make that big of a difference thanks again

 

[Dr.Peterson]

It occurred to me that we should graph the function so you can see just how sensitive the inverse is (that is, how little the function varies in the vicinity of t=3:


[MATH]f^{-1}(0.83)[/MATH] is indeed about 0.92!