MYTUTOR SUBJECT ANSWERS

1270 views

Let f(x) and g(x) be two odd functions defined for all real values of x. Given that s(x)=f(x)+g(x), prove that s(x) is also an odd function.

We recall that a function f(x) is said to be an odd function when f(-x)=-f(x).

We are told that f(x) and g(x) are odd functions, so we know from the above definition that:

1. f(-x)=-f(x)

2. g(-x)=-g(x)

Solution

We want to show that s(x) is an odd function. In other words, we want to show that s(-x)=-s(x) (that it satisfies the above definition).

We are told that s(x)=f(x)+g(x), so substituting x for -x, we get that

s(-x)=f(-x)+g(-x)

=-f(x)-g(x) (using 1 and 2)

=-(f(x)+g(x))

=-s(x) as required!

We have now shown that s(-x)=-s(x) and thus we have proven that s(x) is indeed an odd function.

Keir H. A Level Maths tutor, GCSE Maths tutor

1 year ago

Answered by Keir, an A Level Maths tutor with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

424 SUBJECT SPECIALISTS

£20 /hr

George F.

Degree: Physics (Masters) - Durham University

Subjects offered:Maths, Physics+ 2 more

Maths
Physics
Further Mathematics
Chemistry

“A third year, first class student with a love for my subject. I will do as much as I can to help you reach your goals!”

£30 /hr

Michael D.

Degree: Manufacturing Engineering and Management (Masters) - Cambridge University

Subjects offered:Maths, Physics+ 4 more

Maths
Physics
Further Mathematics
Design & Technology
-Personal Statements-
-Oxbridge Preparation-

“Enthusiastic maths tutor. Tailors tuition to your learning pace and style to build confidence and develop key maths skills and exam technique.”

Trusted by schools

|  6 completed tutorials

£20 /hr

Jessica P.

Degree: Veterinary Science (Bachelors) - Bristol University

Subjects offered:Maths, Science+ 5 more

Maths
Science
Physics
Chemistry
Biology
.BMAT (BioMedical Admissions)
-Personal Statements-

“Veterinary student at the University of Bristol with a background in science and maths, and experience in a summer language school.”

About the author

Keir H.

Currently unavailable:

Degree: Mathematics (Bachelors) - York University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

MyTutor guarantee

You may also like...

Other A Level Maths questions

Find the positive value of x such that log (x) 64 = 2

What is a complex number?

How do you find the possible values of cos(x) from 5cos^2(x) - cos(x) = sin^2(x)?

How to complete the square?

View A Level Maths tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok