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# Precalculus questions with polynomials, exponentials, etc.

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1.) If f(x) = x^3 + 3x^2 - 1, which of these is true?
I. f has domain all real numbers
II. f is a 1-1 function
III. f is onto the set of real numbers

a. Only one (could be any one
b. I and II
c. II and II
d. I and II
e. All three

2) solve e^x +2x =7

3) If log 3 = 1.4 and log5 = 3.6, find log 45

4) Find the period of f(x)= 3-2cos(3x + &#960;)

5) find csc(arctan 8/15)

6) for x ?[0, 2&#960;), solve: cos2x = cosx

https://brainmass.com/math/basic-algebra/precalculus-questions-polynomials-exponentials-311534

#### Solution Preview

1.) If f(x) = x^3 + 3x^2 - 1, which of these is true?
I. f has domain all real numbers
This is true because you can substitute any real number in for x and the value of f will still be a real number.
II. f is a 1-1 function
This is not true. The graph of this function does not pass the horizontal line test. If you draw a horizontal line across this function, it will cross more than once when the line is drawn at certain positions.
III. f is onto the set of real numbers
This is true. The range of this function contains all real numbers so this function is onto.