A community for students.
Here's the question you clicked on:
 0 viewing
jmallis
 one year ago
Determine whether the function is onetoone.
f(x)=(x5)^3
jmallis
 one year ago
Determine whether the function is onetoone. f(x)=(x5)^3

This Question is Closed

Jasmineflvs
 one year ago
Best ResponseYou've already chosen the best response.1Horizontal Line Test • If some horizontal line intersects the graph of the function more than once, then the function is not onetoone. • If no horizontal line intersects the graph of the function more than once, then the function is onetoone. What are OneToOne Functions? Algebraic Test Definition 1. A function f is said to be onetoone (or injective) if f(x1) = f(x2) implies x1 = x2. Lemma 2. The function f is onetoone if and only if 8x1, 8x2, x1 6= x2 implies f(x1) 6= f(x2). Examples and CounterExamples Examples 3. • f(x) = 3x − 5 is 1to1. • f(x) = x2 is not 1to1. • f(x) = x3 is 1to1. • f(x) = 1 x is 1to1. • f(x) = xn − x, n > 0, is not 1to1. Proof. • f(x1) = f(x2) ) 3x1 − 5 = 3x2 − 5 ) x1 = x2. In general, f(x) = ax − b, a 6= 0, is 1to1. • f(1) = (1)2 = 1 = (−1)2 = f(−1). In general, f(x) = xn, n even, is not 1to1. • f(x1) = f(x2) ) x31 = x32 ) x1 = x2. In general, f(x) = xn, n odd, is 1to1. • f(x1) = f(x2) ) 1 x1 = 1 x2 ) x1 = x2. In general, f(x) = x−n, n odd, is 1to1. • f(0) = 0n − 0 = 0 = (1)n − 1 = f(1). In general, 1to1 of f and g does not always imply 1to1 of f + g. Properties of OneToOne Functions Properties Properties If f and g are onetoone, then f g is onetoone. Proof. f g(x1) = f g(x2) ) f(g(x1)) = f(g(x2)) ) g(x1) = g(x2) ) x1 = x2. Examples 4. • f(x) = 3x3 − 5 is onetoone, since f = g u where g(u) = 3u − 5 and u(x) = x3 are onetoone. • f(x) = (3x − 5)3 is onetoone, since f = g u where g(u) = u3 and u(x) = 3x − 5 are onetoone. • f(x) = 1 3x3−5 is onetoone, since f = g u where g(u) = 1 u and u(x) = 3x3 − 5 are onetoone. 2
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.