$$\frac{3}{4} \neq \frac{8}{15}$$

Question 1

Simplify the expression $$\left( \frac{4}{-7} \right).$$

Accepted Answer

$$-\frac{4}{7}$$

Question 2

Evaluate $$-\frac{5}{(-1)}.$$

Accepted Answer

$$5$$

Question 3

Simplify $$2 - \frac{3}{2} = \frac{7}{4}.$$

Accepted Answer

$$\frac{7}{4}$$

Question 4

Express $$\frac{824,075}{100,000} as a $$decimal.

Accepted Answer

$$8.24075$$

Question 5

Solve for $$x$$: $$3(2x-1) - 5(-2x+3) = 3(x-2).$$

Accepted Answer

$$x = 0$$

Question 6

Let $$f(x) = 2x^2$ and g(x$$) = $$3x^4$$ - $$2x^2 + 2$. What is (g/f)(x$$)$$?

Accepted Answer

$$\frac{3x^4$ - 2x^2$ + 2}{2x^2$}$$

Question 7

Let $$f(x) = x^2$ + 2$$ and $$g(x) = 1x - 2. $$What is $$(f \circ g)(x)$$?

Accepted Answer

$$(x - 2)^2$ + 2$$

Question 8

Let $$h(x) = (7 - 2x)^2$. Find f(x$$)$$ and g(x$$)$$ such that h(x) = (f$$ \circ g)(x)$$, with f(x$$) 
eq x$$ and g(x$$) 
eq x$$.

Accepted Answer

$$f(x) = x^2$,\ g(x) = 7 - 2x$$

Question 9

Let $$h(x) = \frac{1}{(2x + 5)^2$}. $$Find $$f(x)$$ and $$g(x)$$ such that $$h(x) = (f \circ g)(x)$$, with $$f(x) 
eq x$$ and $$g(x) 
eq x.$$

Accepted Answer

$$f(x) = \frac{1}{x^2$},\ g(x) = 2x + 5$$

Question 10

Let $$h(x) = \frac{2x + 1}{\sqrt{x - 1}}. $$Find $$f(x)$$ and $$g(x)$$ such that $$h(x) = (f \circ g)(x)$$, with $$f(x) 
eq x$$ and $$g(x) 
eq x.$$

Accepted Answer

$$f(x) = \frac{2x + 1}{x},\ g(x) = \sqrt{x - 1}$$

Question 11

Solve the equation $$(x + 4)(x - 2) = 0.$$

Accepted Answer

$$x = -4 or$$ $$x = 2$$

Question 12

Solve the equation $$3x^2 - 15 = 0$.

Accepted Answer

$$x = \pm \sqrt{5}$$

Question 13

Solve the equation $$2x^2 = 4x$.

Accepted Answer

$$x = 0 or$$ $$x = 2$$

Question 14

Solve the equation by factoring: $$x^2 - 10x - 24 = 0$.

Accepted Answer

$$x = 12 or$$ $$x = -2$$

Question 15

Solve the equation by factoring: $$6x^2 + 2x = 4$.

Accepted Answer

$$x = 1 or$$ $$x = -\frac{2}{3}$$

Question 16

Solve the equation $$2x^2 - 2x - 5 = 0$ using the quadratic formula.

Accepted Answer

$$x = \frac{2 \pm \sqrt{44}}{4}$$

Question 17

Solve the equation $$x^2 - 8x + 7 = 0$.

Accepted Answer

$$x = 7 or$$ $$x = 1$$

Question 18

Solve the equation $$y^2 + 7y + 12 = 0$.

Accepted Answer

$$y = -3 or$$ $$y = -4$$

Question 19

Solve $$\frac{1}{4} + \frac{1}{2} = \frac{1}{3} + \frac{1}{5}.$$

Accepted Answer

$$\frac{3}{4} 
eq \frac{8}{15}$$

Question 20

Solve $$7 + \sqrt{2x - 5} = 10.$$

Accepted Answer

$$x = 7$$

Question 21

Given $$f(x) = (x + 1)^2$(x + i)^3$x^2$, find the zeros and their multiplicities.

Accepted Answer

$$x = -1 ($$multiplicity 2), $$x = -i ($$multiplicity 3), $$x = 0 ($$multiplicity 2)

College Algebra Exam Practice: Functions, Equations, and Graphs

스터디 가이드 - 연습 문제