Question
In Problems $11-16$, determine whether the given set is a subspace of the vector space $C(-\infty, \infty)$.All functions $f$ such that $f(-x)=f(x)$
Step 1
Let $f$ and $g$ be two functions in the set. Then for all $x$ in $C(-\infty, \infty)$, we have $(f+g)(-x) = f(-x) + g(-x) = f(x) + g(x) = (f+g)(x)$. Therefore, the sum of any two functions in the set is also in the set. Show more…
Show all steps
Your feedback will help us improve your experience
Khoobchandra Agrawal and 53 other Calculus 3 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
In Problems $11-16$, determine whether the given set is a subspace of the vector space $C(-\infty, \infty)$. All functions $f$ such that $f(0)=1$
Vectors
Vector Spaces
In Problems $11-16$, determine whether the given set is a subspace of the vector space $C(-\infty, \infty)$. All functions $f$ such that $f(1)=0$
In Problems $11-16$, determine whether the given set is a subspace of the vector space $C(-\infty, \infty)$. All nonnegative functions $f$
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD
