Question 1

Find all values of $$x$$ satisfying the following conditions: $$y = \frac{x^2$}{2}$$, $$y = x + 3$$, and $$x - y = 1.$$

Accepted Answer

There are no solutions.

Question 2

Simplify and write in the form $$a + bi$$: $$\frac{6 - 8i}{2 + 4i}.$$

Accepted Answer

$$-1 + \frac{7}{5}i$$

Question 3

Solve the quadratic equation: $$2x^2 - 10x = 50$ and find the SUM of the solutions.

Accepted Answer

$$10$$

Question 4

Find the solutions of $$2x^2 - 3x + 4 = 0$.

Accepted Answer

$$\frac{3}{4} \pm \frac{\sqrt{23}}{4}i$$

Question 5

Find all values of $$x$$ satisfying the following conditions: $$y = \frac{2x}{x-1}$$, $$x = 3y$$, and $$x + y = 1.$$

Accepted Answer

There are no solutions.

Question 6

The solution of the equation $$9 - \sqrt{2x} = \sqrt{3x} is$$:

Accepted Answer

$$x = 81$$

Question 7

Solve the equation $$x^2 + 4x - 5 = 0$, and the SUM of the solutions is:

Accepted Answer

$$-4$$

Question 8

Given that $$f(x) = x^2$ + 135$$, find $$f(a) - f(-a). $$

Accepted Answer

$$0$$

Question 9

Which of the following functions is odd?

Accepted Answer

$$f(x) = x^3$ - 2x$$

Question 10

If $$f(x) = 2x^2$ + 3x - 5$$, find $$f(x+h) - f(x). $$

Accepted Answer

$$2h^2 + (4x+3)h$

Question 11

Find an equation for the line passing through $$(2,5)$$ and $$(-4,3). $$

Accepted Answer

$$y = \frac{1}{3}x + \frac{7}{3}$$

Question 12

Find an equation of the line containing the point $$(2, -3)$$ and parallel to the line $$2x - y = 4.$$

Accepted Answer

$$y = 2x - 7$$

Question 13

Find the domain of $$f(x) = \sqrt{x-3}.$$

Accepted Answer

$$[3, \infty)$$

Question 14

For $$f(x) = 2x^2$ + x + 1$$ and $$g(x) = x - 1$$, find $$f(g(2)).$$

Accepted Answer

$$9$$

Question 15

For $$f(x) = x^2$ - 4x + 8$$ and $$g(x) = 2x - 5$$, find $$(g - f)(x). $$

Accepted Answer

$$-x^2 + 6x - 13$

Question 16

Find the inverse of $$f(y) = \frac{2y - 3}{4}.$$

Accepted Answer

$$y^{-1}$$ = \frac{4x + 3}{2}$$

Question 17

How can the graph $$y = 2|x - 4| - 5 be $$obtained from the graph $$y = |x|$$?

Accepted Answer

Stretched by factor 2 then shifted right 4 units and down 5 units.

College Algebra: Comprehensive Study Guide and Practice Questions

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