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Precalculus : Pre-Calculus

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12 Diagnostic Tests 380 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1101 : Pre Calculus

Given f(x) and g(x) ,

f(x)=x^2-3x+7

g(x)=2x^3+5x^2-26

Complete the operation given by g(x)-f(x) .

Possible Answers:

2x^3+4x^2+3x-33

2x^3+4x^2-33

2x^3+4x^2+3x-43

6x^3+3x-33

Correct answer:

2x^3+4x^2+3x-33

Explanation:

Given f(x) and g(x)

f(x)=x^2-3x+7

g(x)=2x^3+5x^2-26

Complete the operation given by g(x)-f(x) .

Begin by realizing what this is asking. We need to combine our two functions in such a way that we find the difference between them.

When doing so remember to distribute the negative sign that is in front of f(x) to each term within the polynomial.

$\\(2x^3+5x^2-26)-(x^2-3x+7)\\ \\=2x^3+5x^2-26-x^2+3x-7\\ \\=2x^3+4x^2+3x-33$

So, by simplifying the expression, we get our answer to be:

2x^3+4x^2+3x-33

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Example Question #12 : Add, Subtract, Multiply, And Divide Functions

Given f(x) and g(x) ,

f(x)=x^2-3x+7

g(x)=2x^3+5x^2-26

Evaluate and simplify .

Possible Answers:

4x^3+11x^2-3x-45

4x^3-11x^2-45

4x^3+9x^2-3x-45

4x^3+11x^2-3x-59

Correct answer:

4x^3+11x^2-3x-45

Explanation:

Given f(x) and g(x) ,

f(x)=x^2-3x+7

g(x)=2x^3+5x^2-26

Evaluate and simplify .

Begin by multiplying g(x) by 2:

2g(x)=2(2x^3+5x^2-26)=4x^3+10x^2-52

Next, add f(x) to what we got above and combine like terms.

$\\4x^3+10x^2-52+(x^2-3x+7)\\ \\=4x^3=10x^2+x^2-3x-52+7\\ \\=4x^3+11x^2-3x-45$

This makes our answer

4x^3+11x^2-3x-45 .

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Example Question #13 : Algebra Of Functions

Given y(t) and b(t) , find y(t)*b(t) .

y(t)=t^3-8t

b(t)=5t^7+8t^2

Possible Answers:

$15t^{10}-45t^8+18t^5-16t^3$

$5t^{10}-40t^8+8t^5$

$5t^{21}-40t^{15}+8t^6-64t^2$

$5t^{10}-40t^8+8t^5-64t^3$

Correct answer:

$5t^{10}-40t^8+8t^5-64t^3$

Explanation:

Given y(t) and b(t) , find y(t)*b(t) .

y(t)=t^3-8t

b(t)=5t^7+8t^2

To complete this problem, we need to recall FOIL. FOIL states to multiply the terms in each binomial together in the order of first, outer, inner, and last.

$y(t)*b(t)=(t^3-8t) (5t^7+8t^2)={\color{Blue} t^3*5t^7}+{\color{Red} t^3*8t^2}+{\color{Magenta} -8t*5t^7}+{\color{DarkOrange} -8t*8t^2}$

${\color{Blue} t^3*5t^7}+{\color{Red} t^3*8t^2}+{\color{Magenta} -8t*5t^7}+{\color{DarkOrange} -8t*8t^2}=5t^{10}+8t^5-40t^8-64t^3$

We have no like terms to combine, so our answer is:

$5t^{10}-40t^8+8t^5-64t^3$

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Example Question #12 : Algebra Of Functions

Determine $\small f+g$

$\small f(x)=3x$ and $\small g(x)=7$

Possible Answers:

$\small f+g=3x+7$

$\small f+g=4x$

$\small f+g=10$

$\small f+g=10x$

Correct answer:

$\small f+g=3x+7$

Explanation:

f+g is defined as the sum of the two functions f(x) and $\small g(x)$ .

As such

$\small f+g=f(x)+g(x)=3x+7$

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Example Question #12 : Algebra Of Functions

Determine $\small f+g$

$\small \small f(x)=5x^2$ and $\small \small g(x)=6x^2$

Possible Answers:

$\small \small f+g = 11x^2$

$\small \small \small f+g = \frac{5}{6}$

$\small \small \small f+g = 30x^4$

$\small \small \small f+g = x^2$

Correct answer:

$\small \small f+g = 11x^2$

Explanation:

f+g is defined as the sum of the two functions f(x) and $\small g(x)$ .

As such

$\small \small f+g=f(x)+g(x)=5x^2+6x^2=11x^2$

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Example Question #1101 : Pre Calculus

Add the following functions:

(x^2-3x-1)+(4x^2+5x+2)

Possible Answers:

-3x^2-8x-3

5x^2+2x+1

Correct answer:

5x^2+2x+1

Explanation:

To add, simply combine like terms. Thus, the answer is:

5x^2+2x+1

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Example Question #1107 : Pre Calculus

Given the functions: f(x) = 3 and g(x) = 6 , what is f(3)-g(5) ?

Possible Answers:

Correct answer:

Explanation:

For f(3) , substitute the value of inside the function for f(x) and evaluate.

f(3) = 3

For g(5) , substitute the value of inside the function for g(x) and evaluate.

f(5)= 6

Subtract f(3)-g(5) .

f(3)-g(5) = 3-6 = -3

The answer is:

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Example Question #1102 : Pre Calculus

Simplify $f(x)\cdot g(x)$ given,

f(x)=x^2+2

g(x)=x+6

Possible Answers:

x^3+12

x^2+x+8

x^3+6x^2+2x+12

6x^2+12x

Correct answer:

x^3+6x^2+2x+12

Explanation:

To solve $f(x)\cdot g(x)$ , simply multiply your two functions. Thus,

$\\ f(x)\cdot g(x)=(x^2+2)(x+6)=(x^2)(x)+(6)(x^2)+(2)(x)+(2)(6) \\ \\ =x^3+6x^2+2x+12$

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Example Question #23 : Algebra Of Functions

If $f(x)=\frac{4x-1}{x^2}$ and g(x)=x+1 , find $f\cdot g(x)$ .

Possible Answers:

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

$\frac{x+3}{x^2+2x+1}$

$\frac{4x+3}{2x+1}$

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

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

Correct answer:

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

Explanation:

To solve this problem, you must plug in the g function to wherever you see x in the f function. When you plug that in, it looks like this: $\frac{4(x+1)-1}{(x+1)^2}$ . Then simplify so that your answer is: $\frac{4x+3}{x^2+2x+1}$ .

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Example Question #153 : Functions

Find $\left(\frac{f}{g}\right)(x)$ given $f(x)=\frac{1}{x^3}$ and $g(x)=\frac{1}{x^2}$ .

Possible Answers:

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

The answer is not present.

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

$(\frac{f}{g})(x)=\frac{1}{x}$

$(\frac{f}{g})(x)=\frac{1}{x^6}$

Correct answer:

$(\frac{f}{g})(x)=\frac{1}{x}$

Explanation:

The problem is asking to find the composite function that results when f(x) is divided by g(x).

When dividing fractions, it is important to remember to multiply by the inverse.

$\left(\frac{f}{g}\right)(x)=\frac{\frac{1}{x^3}}{\frac{1}{x^2}}=\frac{1}{x^3}*\frac{x^2}{1}=\frac{1}{x}$

Cross cancel the exponents leaving only one "x" in the bottom.

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Precalculus : Pre-Calculus

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #1101 : Pre Calculus

Example Question #12 : Add, Subtract, Multiply, And Divide Functions

Example Question #13 : Algebra Of Functions

Example Question #12 : Algebra Of Functions

Example Question #12 : Algebra Of Functions

Example Question #1101 : Pre Calculus

Example Question #1107 : Pre Calculus

Example Question #1102 : Pre Calculus

Example Question #23 : Algebra Of Functions

Example Question #153 : Functions

All Precalculus Resources

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