Calculus
posted by C .
Determine whether or not each of the following functions is invertible. Give your reasons for believing the function is invertible or not.
Please check this for me. I am not sure if I am adequately explaining my answer and if my answer is right.
a) y= log10(1 + 1/x)
y'= ((1/(1 + 1/x)*ln(10)) * (1/x^2))
I plugged 100 and 100 into the derivative and got 4.3 X 10^5 and  4.4 X 10^5
NOT INVERTIBLE because I plugged in 0.5 and got a positive answer, so the derivative is then increasing and decreasing, right? The function also has two inflection points at x=0 and x=1
b) y= e^(x^2  5x + 6)
y'= (e^(x^2  5x + 6) * (2x  5))
I plugged 10 and 10 into the derivative and got 3.1 X 10^25 and 1.4 X 10^69
The function is increasing and decreasing, so there is a max and min value and there is more than one xvalue for the yvalue, thus NOT INVERTIBLE.

Let's start with b, the answer of which is correct: it is not invertible.
Domain of the function is ℝ since it is the exponential function raised to a polynomial power.
If it were invertible, as you mentioned, the derivative would not change sign.
Change in sign of the derivative implies that on each side of the extremum, the function will take on the same value within its domain, which renders the function not invertible. In other words, it does not pass the horizontal line test.
For part a.
Again, we have to first determine the domain of the function:
Since log functions cannot take on negative values, we determine that the domain of the function is limited to the range of x where the expression inside the log is nonnegative, namely (&infin,1)∪(0,∞).
Now we have to look at the function within its domain.
We find that the function is monotonically decreasing throughout its domain, within which it satisfies the horizontal line test.
Would you therefore reevaluate your answer?
To help make your decision, you can have some thoughts on two things:
1. look at the graph of the function:
http://img853.imageshack.us/i/1300926177.png/
2. Find its inverse:
f1(x)=1/(10^x1)
which is a perfectly legitimate function undefined at x=0.
Respond to this Question
Similar Questions

Algebra
Let A and B be n x n matrices, assume AB is invertible and show that both A and B are invertible. what? 
College Math : Linear Algebra
Suppose A is a square matrix satisfying the equation A^3  2I = 0. Prove that A and (A  I) respectively are invertible. (the hint is to find an explicit equation for A^1. To prove A is invertible, this is what I did although I don't … 
LINEAR ALGEBRA
How to prove or disprove (a)if A has a zeronentryonthe diagonal then A is not invertible (b)if Ais not invertible then for every matrix B, AB is not invertible (c)if A is a nonzero 2X2 matrix such that A^2+A=0, then A is invertible 
Calc. checking answer
Determine whether or not each of the following functions is invertible. Give your reasons for believing the function is invertible or not. Please check this for me. I am not sure if I am adequately explaining my answer and if my answer … 
linear algebra
1)If A is an invertible matrix and k is a positive integer, then (A^k)^1 = (A^1)^k note: ^ stand for power, 1 stand for inverse of A 2)If A is an invertible matrix, then (transpose of A)^1 =transpose of(A^1) 3)Prove A^2 = A, then … 
Trig
Let f and g be two invertible functions such that f^1(x)=5/x+4 and g(x)=4(x2). Find f(g(5)). Show your steps please so I can see how to do it. Thank you! :) 
Math
Determine whether each of the following function is invertible and very briefly explain your answer. a) The function that pairs the number of days since your birth with your age in years. b) The function that pairs the speed of your … 
Algebra
Some functions that aren't invertible can be made invertible by restricting their domains. For example, the function x^2 is invertible if we restrict x to the interval [0,inf), or to any subset of that interval. In that case, the inverse … 
math
Some functions that aren't invertible can be made invertible by restricting their domains. For example, the function x^2 is invertible if we restrict x to the interval [0,\inf), or to any subset of that interval. In that case, the … 
Math
Determine whether or not the given linear transformation is invertible. If it is invertible, compute its inverse. (If the transformation is not invertible, enter IMPOSSIBLE. Use theta for θ.) Tθ:R2→R2, the reflection …