next up previous
Next: About this document ... Up: lab_template Previous: Inverse Functions

Exercises

  1. Solve for x in the equations.

    1. \begin{displaymath} \ln(x)+x^x=e \end{displaymath}


    2. \begin{displaymath} \ln(x)+\ln(x+1)=2 \end{displaymath}


    3. \begin{displaymath} 3^x+2^x=5^x \end{displaymath}


    4. \begin{displaymath} log_{10}(100)=\frac{\sqrt{x}}{7} \end{displaymath}


  2. \begin{displaymath} f(x)=\frac{ln(x-2)}{x} \end{displaymath}


    \begin{displaymath} g(x)=\frac{(x+5)^3}{24}+4 \end{displaymath}

    A
    Plot f(x) on the domain $0 \leq x \leq 100$. Plot g(x) on the domain $-15 \leq x\leq 10$. Which function is not invertible and why?
    B
    Find the inverse of the invertible function.(Note, there will be one non-imaginary result, that should be your inverse.)
    C
    Plot the function and its inverse along with the line $y=x$ on the intervals $-5 \leq x \leq 50$ and $-5 \leq y \leq 50$.

Jane E Bouchard
2010-04-12