Muft Shiksha
Update

Muft Shiksha™ एक 100% Free Education Portal है 🇮🇳, जिसका उद्देश्य Class 9–12 के हर विद्यार्थी तक High-Quality Education को पूरी तरह मुफ्त पहुँचाना है। 🇮🇳 हम मानते हैं कि अच्छी शिक्षा किसी student की आर्थिक स्थिति पर निर्भर नहीं होनी चाहिए। 🇮🇳 हर विद्यार्थी को वही Quality Study Material, MCQs, Quizzes, Exam Preparation, Concept-Based Learning और Bilingual Support मिलना चाहिए, जो आमतौर पर महंगी Coaching या Premium Platforms में मिलता है। Muft Shiksha™ 🇮🇳 इसी सोच के साथ बनाया गया है

Subjects
Class 12MathematicsRelations and FunctionsOne-one functionExpert
0 reads0 ratings0 helpful

If (f:\mathbb{R}\to(0,\infty)), (f(x)=e^{x^2}), why is (f) not one-one?

Answer and explanation

Correct answer: Because (f(1)=f(-1))

Step 1: (x^2) has the same value at (x) and (-x). Step 2: Hence (f(1)=e^1) and (f(-1)=e^1), while (1\ne-1). Step 3: Even with an exponential outer function, an even inner expression can break one-one nature.

Related tags

ExponentialEven FunctionNot One-OneCounterexampleOne One FunctionRelations And FunctionsMathematicsClass 12 Mcq
सुधार सुझाएँ / Earn

Was this question useful?

No ratings yetWrite a review / Rate this question

Student Reviews

No published reviews yet.

KEEP PRACTISING

10 more MCQs
  1. 1Which statement is true for a one-one function?
  2. 2If (f(2)=5) and (f(3)=5), what can be said about (f)?
  3. 3If (f:\mathbb{R}\to\mathbb{R}) and (f(x)=2x+1), what type of function is (f)?
  4. 4If (f:\mathbb{R}\to\mathbb{R}) and (f(x)=7), what type of function is (f)?
  5. 5If (f:\mathbb{R}\to[0,\infty)) and (f(x)=|x|), what type of function is (f)?
  6. 6If (f:\mathbb{R}\to(0,\infty)) and (f(x)=e^x), what type of function is (f)?
  7. 7If (f:(0,\infty)\to\mathbb{R}) and (f(x)=\log x), which statement about (f) is correct?
  8. 8If (f:\mathbb{R}\to\mathbb{R}) and (f(x)=3x-5), what follows from (f(a)=f(b))?
  9. 9Which example proves that (f(x)=x^2+1) is not one-one on real numbers?
  10. 10If (f:\mathbb{N}\to\mathbb{N}) and (f(n)=n+4), what type of function is (f)?
Found an issue? Help improve this questionMy reports and replies

Add Muft Shiksha to your Home Screen

In Safari, tap Share, then Add to Home Screen.