# Math Worksheet

MATH 107 Quiz 5

Each question is worth 5 points. Questions 1 – 5 are multiple choice; you do not need to show your work. Short answers for Questions 6 – 10; show your work to earn full credit – highlight answers in yellow or draw a box around the answer. You can insert additional lines if needed.

Leave answers in exact form unless otherwise directed to approximate the results. Write all fractions in lowest form and round decimals to hundredths. Write answers using positive exponents except when using scientific notation. Simplify all radicals and rationalize the denominators. Write complex numbers in the form a + bi. Applied problems must have the variables identified and an equation for full credit.

MULTIPLE CHOICE Check the box of the one alternative that best completes the statement or answers the question.

1.) Find f(x) and g(x) such that h(x) = (f ∘ g)(x) if

☐ f(x) = 5, g(x) =

☐ f(x) = , g(x) = 6x + 3

☐ f(x) = , g(x) = 5

☐ f(x) = , g(x) = 6x + 3

☐ None of these

2.) Determine if f(x) = 2×2 + 6, x ≥ 0 is one-to-one. If it is one-to-one, find a formula for the inverse.

☐ Not one-to-one

☐ None of these

3.) Write as an expression containing a single radical and simplify.

☐ None of these

4.) Solve the exponential equation.

☐ 3

☐ 1

☐ 7

☐ None of these

5.) Solve the logarithmic equation.

☐ 64

☐ 81

☐ None of these

2

6.) Find (f ∘ g)(x) if and

7.) Given that is one-to-one, find a formula for the inverse.

8.) Solve.

9.) Solve the exponential equation.

10.) An earthquake was recorded with an intensity which was 3,981,072 times more powerful than a reference level earthquake, or 3,981,072∙I0. What is the magnitude of this earthquake on the Richter scale? The magnitude on the Richter scale of an earthquake of intensity I is

11) In this Exercise, use the appropriate change of base formula to approximate the logarithm.

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