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\noindent \textbf{Math 1441 Worksheet 0}\\[0.1cm]

\noindent
{\bf 1.} Simply the fraction.
$$(a)\ \frac{1}{2}-\frac{1}{3}\qquad\qquad\qquad\qquad 
(b)\ \frac{2}{5}\cdot\frac{3}{4}\qquad\qquad\qquad\qquad 
(c)\ \frac{\,\frac{5}{4}\,}{\,\frac{3}{2}\,}$$\\[0.5cm]

\noindent
{\bf 2.} Expand and simplify. 
$$(x+3)(4x-5)$$\\[0.5cm]

\noindent
{\bf 3.} Factor the expression.
$$4x^2-25$$\\[0.5cm]

\noindent
{\bf 4.} Simplify the rational expression.
$$\frac{x^2+3x+2}{x^2-x-2}$$\\[0.5cm]

\noindent
{\bf 5.} Solve the equation.
$$x^2-x-12=0$$\\[0.5cm]

\noindent
{\bf 6.} Sketch the graph of the function.
$$y=x^2-1$$\\[0.5cm]

\noindent
{\bf 7.} Find the domain of the function.
$$\sqrt{1-x}$$\\[0.5cm]

\noindent
{\bf 8.} If $f(x)=2x-3$ and $g(x)=x^2+2x-1$, find the composition.
$$f(g(x))$$

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Answers:

(1)\ $(a)\ \frac{1}{6}\qquad (b)\ \frac{3}{10}\qquad (c)\ \frac{5}{6}$

(2)\ $4 x^2 + 7 x -15$

(3)\ $(2x-5)(2x+5)$

(4)\ $\frac{x+2}{x-2}$

(5)\ $-3,4$

(7)\ $(-\infty,1]$

(8)\ $2x^2+4x-5$

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