Math Insight

Gateway exam, version 1391

Math 1241, Fall 2020
Name:
Section:
Table/group #:
Total points: 10
Time limit: 50 minutes
  1. Compute the value of $f(f(f(10)))$ for the function $f(x)=3x+4$.

    $f(f(f(10))) =$

  2. Rewrite the expression $$\log{\left (\frac{\sqrt[3]{- 5 y - 6}}{\left(2 y - 2\right)^{\frac{16}{9}}} \right )}$$ in a form with no logarithm of a product, quotient or power. Then, $$\log{\left (\frac{\sqrt[3]{- 5 y - 6}}{\left(2 y - 2\right)^{\frac{16}{9}}} \right )} = A \log \left(2 y - 2\right) + B \log \left(- 5 y - 6\right) + C\log\left(2 y - 2\right),$$ where

    A =

    B =

    C =

  3. Write the function $f(x)=6e^{ 6x+1 }$ in the form $f(x)=Ae^{kx}$.   What are the values of the parameters $A$ and $k$?

    $A=$
    , $k=$

    Need help?

  4. Find the equation for the line through the point $(-3,-9)$ with slope given by $m=-1$

    $y = $

  5. Solve for $x$: \[ x(3-x)=x+2x^2 \]

    $x =$
    (If there is more than one solution, separate solutions by commas.)

  6. Solve the system of equations. \begin{align*} n + 4 s &= -2\\ 2 n + 2 s &= 4 \end{align*}
    $s = $

    $n = $

  7. Simplify the inequality below: \begin{align*} \left|\frac{4 x}{3} + 5\right|<7 \end{align*}


    $\lt x \lt$

  8. Let the variable $x$ be in the range \begin{align*} 1< x <7. \end{align*} If $y= 3 x + 5$, what is the range of the variable $y$?


    $\lt y \lt$

  9. Let $g(x) = 4 e^{9 x - 4}$ and $h(x) = - 4 x^{2} + x$. What is $g(h(x))$?

    $g(h(x)) = $

    Need help?

  10. Solve the equation $-6\left(x - 4\right) \left(x - 2\right)^{2} \left(x + 8\right) \left(9 x - 1\right) =0$.

    The solutions are $x = $

    If there are more than one solution, separate answers by commas