Determine-all-function-f-R-R-which-satisfy-f-a-x-f-a-x-4ax-for-all-real-a-and-x- Tinku Tara June 4, 2023 Relation and Functions 0 Comments FacebookTweetPin Question Number 120300 by bemath last updated on 30/Oct/20 Determineallfunctionf:R→Rwhichsatisfyf(a+x)−f(a−x)=4axforallrealaandx. Commented by benjo_mathlover last updated on 30/Oct/20 letf(x)=px2+qx+rf(a+x)=p(a2+2ax+x2)+qx+aq+rf(a+x)=px2+(2ap+q)x+a2p+aq+rf(a−x)=p(a2−2ax+x2)+aq−qx+rf(a−x)=px2−(2ap+q)x+a2p+aq+rf(a+x)−f(a−x)=(4ap+2q)x≡4ax→4ap+2q=4a;4ap−4a=−2q4a(1−p)=2q⇒1−p=q2a⇒p=1−q2a=2a−q2af(x)=(2a−q2a)x2+qx+r Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: Question-54765Next Next post: A-stone-is-thrown-vertically-upwards-from-a-cliff-20m-high-After-a-time-of-3-s-it-passes-the-edge-of-the-cliff-on-its-way-down-Calculate-a-the-speed-of-projection-b-the-speed-when-it-hits-the-grou Leave a Reply Cancel replyYour email address will not be published. Required fields are marked *Comment * Name * Save my name, email, and website in this browser for the next time I comment.