How to Multiply and Dividing Functions

How to Multiply and Dividing Functions

Multiplying and dividing functions is similary to multiplying and dividing polynomials. Learn how to multiply and divide functions in this post. 

Related Topics

Step by step guide to Multiplying and Dividing Functions

  • Just like we can multiply and divide numbers, we can multiply and divide functions. For example, if we had functions \(f\) and \(g\), we could create two new functions: \(f × g\), and \(\frac{f}{g}\).

Multiplying and Dividing Functions – Example 1:

\(g(x)=x+1, f(x)=x-2\), Find: \((g.f)(2)\)

Solution:

\((g.f)(x)=g(x).f(x)=(x+1)(x-2)=x^2-2x+x-2=x^2-x-2 \)
Substitute \(x\) with \(2\):
\((g.f)(x)=x^2-x-2=(2)^2-2-2=4-2-2=0 \)

Multiplying and Dividing Functions – Example 2:

\(f(x)=x-2, h(x)=x+8\), Find: \((\frac{f}{h})(-1)\)

Solution:

\((\frac{f}{h})(x)=\frac{f(x)}{h(x)} =\frac{x-2}{x+8} \)
Substitute x with \(-1: (\frac{f}{h})(x)=\frac{x-2}{x+8}=\frac{(-1)-2}{(-1)+8}=\frac{-3}{7}=-\frac{3}{7} \)

Multiplying and Dividing Functions – Example 3:

\(g(x)=-x-2, f(x)=2x+1\), Find: \((g.f)\)

Solution:

\((g.f)(x)=g(x).f(x)=(-x-2)(2x+1)=-2x^2-x-4x-2=-2x^2-5x-2 \)

Multiplying and Dividing Functions – Example 4:

\(f(x)=x+4, h(x)=5x-2\), Find: \((\frac{f}{h})\)

Solution:

\((\frac{f}{h})(x)=\frac{f(x)}{h(x)} =\frac{x+4}{5x-2} \)

Exercises for Multiplying and Dividing Functions

Perform the indicated operation.

  • \(\color{blue}{g(a) = 2a – 1 \\ h(a) = 3a – 3 \\ Find \ (g.h)(– 4) } \\\ \)
  • \(\color{blue}{f(x) = 2x^3 – 5x^2 \\ g(x) = 2x – 1 \\ Find \ (f.g)(x)} \\\ \)
  • \(\color{blue}{g(t) = t^2 + 3 \\ h(t) = 4t – 3 \\ Find \ (g.h)(– 1)} \\\ \)
  • \(\color{blue}{g(n) = n^2 + 4 + 2n \\ h(n) = – 3n + 2 \\ Find \ (g.h)(1)} \\\ \)
  • \(\color{blue}{g(a) = 3a + 2 \\ f(a) = 2a – 4 \\ Find (\frac{g}{f})(3) } \\\ \)
  • \(\color{blue}{f(x) = 3x – 1 \\ g(x) = x^2 – x \\ Find \ (\frac{f}{g})(x)}\)

Download Multiplying and Dividing Functions Worksheet

Answers

  • \(\color{blue}{135}\)
  • \(\color{blue}{4x^4 – 12x^3 + 5x^2}\)
  • \(\color{blue}{-28}\)
  • \(\color{blue}{-7}\)
  • \(\color{blue}{\frac{11}{2}} \\\ \)
  • \(\color{blue}{\frac{3x-1}{x^2-x}}\)

Related to "How to Multiply and Dividing Functions"

Top 10 Tips to ACE the CBEST Math Test
Top 10 Tips to ACE the CBEST Math Test
Top 10 Tips You MUST Know to Retake the CBEST Math
Top 10 Tips You MUST Know to Retake the CBEST Math
Top 10 Tips to Overcome CBEST Math Anxiety
Top 10 Tips to Overcome CBEST Math Anxiety
Top 10 Tips to Create a CBEST Math Study Plan
Top 10 Tips to Create a CBEST Math Study Plan
How is the CBEST Test Scored?
How is the CBEST Test Scored?
Top 10 Tips You MUST Know to Retake the PERT Math
Top 10 Tips You MUST Know to Retake the PERT Math
Top 10 Tips to Overcome PERT Math Anxiety
Top 10 Tips to Overcome PERT Math Anxiety
Top 10 Tips to Create a PERT Math Study Plan
Top 10 Tips to Create a PERT Math Study Plan
Top 10 Tips You MUST Know to Retake the ASTB-E Math
Top 10 Tips You MUST Know to Retake the ASTB-E Math
Top 10 Tips to Overcome ASTB Math Anxiety
Top 10 Tips to Overcome ASTB Math Anxiety

Leave a Reply

Your email address will not be published. Required fields are marked *

36% OFF

Download Instantly

X

How Does It Work?

Find Books

1. Find eBooks

Locate the eBook you wish to purchase by searching for the test or title.

add to cart

2. Add to Cart

Add the eBook to your cart.

checkout

3. Checkout

Complete the quick and easy checkout process.

download

4. Download

Immediately receive the download link and get the eBook in PDF format.

Why Buy eBook From Effortlessmath?

Save money

Save up to 70% compared to print

Instantly download

Instantly download and access your eBook

help environment

Help save the environment

Access

Lifetime access to your eBook

Test titles

Over 2,000 Test Prep titles available

Customers

Over 80,000 happy customers

Star

Over 10,000 reviews with an average rating of 4.5 out of 5

Support

24/7 support

Anywhere

Anytime, Anywhere Access

Find Your Test

Schools, tutoring centers, instructors, and parents can purchase Effortless Math eBooks individually or in bulk with a credit card or PayPal. Find out more…