Question 1

Given the function $$f(x) = \sqrt{2x - 3}$$, what is the domain of $$f(x)$$?

Accepted Answer

$$x \geq 1.5$$

Question 2

Solve for $$x$$: $$5x - 2 = 3x + 6$$

Accepted Answer

$$x = 2$$

Question 3

If $$f(x) = 2x^2$ - 5x + 3$$, what is $$f(-2)$$?

Accepted Answer

$$21$$

Question 4

Which of the following is the solution set for $$|x - 4| = 7$$?

Accepted Answer

$$x = -3$$ and $$x = 11$$

Question 5

A car rental company charges a flat fee of $$\25$ plus $$\$$0.15$$ per mile driven. If the total cost is $$\40$, how many miles were driven?

Accepted Answer

$$75$$

Question 6

Simplify: $$\dfrac{2x^2$ - 8}{x^2$ - 4}$$

Accepted Answer

Question 7

Which of the following is the solution to $$\sqrt{x + 5} = 4$$?

Accepted Answer

$$x = 11$$

Question 8

If $$f(x) = 3x - 7$$ and $$g(x) = x^2$, what is (f$$ \circ g)(2)$$?

Accepted Answer

$$5$$

Question 9

Solve for $$x$$: $$\dfrac{x}{3} + 2 = 5$$

Accepted Answer

$$x = 9$$

Question 10

Which of the following is the correct factorization of $$x^2 - 9$?

Accepted Answer

$$(x - 3)(x + 3)$$

Question 11

A population of bacteria doubles every 3 hours. If the initial population is $$500$$, what will the population be after $$9$$ hours?

Accepted Answer

$$4000$$

Question 12

Solve for $$x$$: $$2x^2 - 8x = 0$

Accepted Answer

$$x = 0$$ and $$x = 4$$

Question 13

Which of the following is the solution to $$3(x - 2) = 2x + 5$$?

Accepted Answer

$$x = 7$$

Question 14

If $$f(x) = x^2$ - 4x + 7$$, what is the vertex of the parabola?

Accepted Answer

$$(2, 3)$$

Question 15

Which of the following is the solution set for $$x^2 = 25$?

Accepted Answer

$$x = 5$$ and $$x = -5$$

Question 16

A chemist mixes a solution that is $$30\%$$ acid with one that is $$10\%$$ acid to get $$20$$ liters of a $$20\%$$ acid solution. How many liters of the $$30\%$$ solution are used?

Accepted Answer

$$10$$

Question 17

Which of the following is the correct solution to $$x^2 + 6x + 9 = 0$?

Accepted Answer

$$x = -3$$

Question 18

If $$f(x) = 2x + 1$$ and $$g(x) = x - 3$$, what is $$f(g(4))$$?

Accepted Answer

$$3$$

Question 19

Which of the following is the solution to $$\dfrac{2x - 4}{x} = 0$$?

Accepted Answer

$$x = 2$$

Question 20

A ball is thrown upward with an initial velocity of $$32 ft/s $$from a height of $$48 ft. $$Its height after $$t$$ seconds is given by $$h(t) = -16t^2$ + 32t + 48. $$When does the ball reach its maximum height?

Accepted Answer

$$t = 1 s$$

Equations, Inequalities, and Functions: College Algebra Study Notes

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