Wednesday
July 23, 2014

Homework Help: Calculus

Posted by C on Wednesday, March 23, 2011 at 8:22pm.

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

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