Question
Assume that $p$ is a function that is defined for $x>0$ and satisfies $p(a / b)=p(b)-p(a) .$ Prove that $f(x)=p\left(\frac{2-x}{2+x}\right)$ is an odd function.
Step 1
A function $f(x)$ is odd if for all $x$ in the domain of $f$, we have $f(-x) = -f(x)$. We want to prove that $f(x)=p\left(\frac{2-x}{2+x}\right)$ is an odd function. Show more…
Show all steps
Your feedback will help us improve your experience
Noel Aguilar and 81 other Calculus 1 / AB 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
Assume that $p$ is a function that is defined for all $x$. (a) Prove that if $f$ is defined by $f(x)=p(x)+p(-x)$ then $f$ is even. (b) Prove that if $g$ is defined by $g(x)=p(x)-p(-x)$ then $g$ is odd.
Precalculus Review
Real Numbers, Functions and Graphs
Show that $P_{I}(-1)=(-1)^{2}$. Hint: When is $P_{l}(x)$ an even function and when is it an odd function?
SERIES SOLUTIONS OF DIFFERENTIAL EQUATIONS; LEGENDRE POLYNOMIALS; BESSEL FUNCTIONS; SETS OF ORTHOGONAL FUNCTIONS
Legendre's equation
Show that if $f$ is any function, then the function $O$ defined by $$O(x)=\frac{f(x)-f(-x)}{2}$$ is odd.
More on Functions
Symmetry and Transformations
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD