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 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.

  1. 👍 0
  2. 👎 0
  3. 👁 242
  1. 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?

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. History

    1. What has been the most significant effect of artistic development in New Mexico since World War II? Give two reasons to justify your answer. 2. List two factors that contributed to the expansion of Native American voting rights

  2. I Need Help! :'(

    Drag the reasons why Rome was able to expand into the box. a.The maniple was a flexible military unit. b.The Romans stayed isolated from others. c.The Roman soldiers built roads and bridges. d.Rome would give citizenship to loyal

  3. Linear Algebra

    Find conditions on k that will make the matrix A invertible. To enter your answer, first select 'always', 'never', or whether k should be equal or not equal to specific values, then enter a value or a list of values separated by

  4. calculus

    Choose any two specific functions (not already chosen by a classmate) that have inverses. Use your chosen functions to answer any one of the following questions: If the inverses of two functions are both functions, will the

  1. PreCalc

    Choose any two specific functions that have inverses. Use your chosen functions to answer any one of the following questions - If the inverses of two functions are both functions, will the inverse of the sum or difference of the

  2. Math

    For each pair of functions give a characteristic that the two functions have in common and a characteristic that distinguishes them. a) f(x)=1/x and g(x)=sinx b) f(x)=x and g(x)=[x] c) f(x)=2^x and g(x)=sinx

  3. Mathematics

    Let f(x) = 3x2– 2x + n and g(x) = mx2 – nx + 2. The functions are combined to form the new functions h(x) = f(x) - g(x) and j(x) = f(x) + g(x). Point (6, 2) is in the function h(x), while the point (-2, 10) is in the function

  4. Math

    Help me for this question on composite functions Does the composition of functions display the commutative property? Give an example of each case to illustrate your answer.

  1. Mathematics

    Given the functions f(x) = 2x + 1 and g(x) = x - 3, determine an equation for (f ∘ g)(x) and (g ∘ f)(x). Determine f(g(5)) and g(f(5)). Determine all values of x for which f(g(x)) = g(f(x)

  2. 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

  3. Math

    Give the domain of the following functions. Give your answer in interval notation. a) f(x)= 5x-2/x^2-5x+6 and b) square root of 5-2x

  4. math

    consider the functions f(x)=x^3-2 and g(x)=3 sqrt x+2: a. find f(g(x)) b. find g(f(x)) c. determine whether the functions f and g are inverse of each other. I have no clue where to even begin!

You can view more similar questions or ask a new question.