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

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 $f(x) = (x + 1)^2(x + i)^3x^2$, 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

Study Guide - Practice Questions