Sunday

April 20, 2014

April 20, 2014

Posted by **C** on Wednesday, March 23, 2011 at 4:19pm.

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 x-value for every y-value, 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 x-value for the y-value, thus NOT INVERTIBLE.

- Calc. checking answer -
**C**, Wednesday, March 23, 2011 at 8:18pmCorrection 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?

**Related Questions**

Calculus - Determine whether or not each of the following functions is ...

LINEAR ALGEBRA - How to prove or disprove (a)if A has a zeronentryonthe diagonal...

College Math : Linear Algebra - Suppose A is a square matrix satisfying the ...

Algebra - Let A and B be n x n matrices, assume AB is invertible and show that ...

Math - Determine whether each of the following function is invertible and very ...

linear algebra - 1)If A is an invertible matrix and k is a positive integer, ...

Trig - Let f and g be two invertible functions such that f^-1(x)=5/x+4 and g(x)=...

math - If A^TA is an invertible matrix, prove that the column vectors of A are ...

Algebra - Right now we are learning about functions, relations, etc. and I am ...

Algebra - Could you please check my work. Determine whether the realtion is a ...