Posted by C on .
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 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 -
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?