Calc. checking answer
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
From this I concluded that no matter what number is plugged into the derivative, the result will be negative. Therefore, there is no maximum or minimum value. The function is only decreasing and there is only one xvalue for every yvalue, and is thus INVERTIBLE. The function has two inflection points at x=0 and x=1 but it should not prevent the function from having an inverse.
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.

Calc. checking answer 
C
Correction to part a) NOT INVERTIBLE because I plugged in 0.5 and got a positive answer, so the derivative is then increasing and decreasing, right?
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 
Calculus
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 … 
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 … 
pre calc
Over which of the following domains is f(x) = csc(0.1x + 1.2) defined at all points and invertible?