Mathematics 131 – Calculus for Physical and Life Sciences 1 Precalculus Diagnostic Quiz – September 7, 2004

Your Name:

Do all work on this sheet (front and back if needed). You have 15 minutes. No calculators on this quiz.

1. Solve for x: 3x^{2} − 21x + 30 = 0.

2. Let f(x) = \sqrt{x − 1} and g(x) = x^{3} + 1. Find f(g(x))? What is the domain of f(g(x))?

3. Simplify and express as a single fraction:

\frac{\frac{x}{\sqrt{x+1}} + \sqrt{x + 1}}{\frac{x}{x^{2}+3}}

4. Let f(x) = x^{2} + 2x. Compute and simplify: f(2 + h) − f(2 − h).