Q76.The domain of f(x) = e2 loge x−(2x+3) (1) R −{−1, 3} (2) (2, ∞) −{3} (3) (−1, ∞) −{3} (4) R −{3}
What This Question Tests
This question primarily tests the understanding of conditions for the existence of logarithmic and rational functions to determine the domain.
Concepts Tested
Formulas Used
log(base a)b implies b > 0 and a > 0, a != 1
📚 NCERT Sections This Tests
1.3 — Define The Following Terms:
Chemistry Class 11 · Chapter 1
1.3 Define the following terms: (i) Mole fraction (ii) Molality (iii) Molarity (iv) Mass percentage.
14.2 — Which Of The Statements Given In Exercise 14.1 Is True For P-Type
Physics Class 12 · Chapter 14
14.2 Which of the statements given in Exercise 14.1 is true for p-type semiconductos.
2.1 — Arrange The Following Metals In The Order In Which They Displace Each Other
Chemistry Class 11 · Chapter 2
2.1 Arrange the following metals in the order in which they displace each other from the solution of their salts. Al, Cu, Fe, Mg and Zn.
📋 Question Details
- Chapter
- Sets Relations Functions
- Topic
- Domain of a function
- Year
- 2023
- Shift
- 29 Jan Shift 1
- Q Number
- Q76
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 2: Relations and Functions
More from this Chapter
Q86.Let R be the real line. Consider the following subsets of the plane R × R. S = {(x, y) : y = x + 1 and 0 < x < 2}, T = {(x, y) : x −y is an integer }. Which one of the following is true? (1) neither S nor T is an equivalence relation on R (2) both S and T are equivalence relations on R (3) S is an equivalence relation on R but T is not (4) T is an equivalence relation on R but S is not
Q91.Let f : N →Y be a function defined as f(x) = 4x + 3, where Y = {y ∈N : y = 4x + 3 for some x ∈N}. Show that f is invertible and its inverse is (1) g(y) = 3y+43 (2) g(y) = 4 + y+34 (3) g(y) = y+34 (4) g(y) = y−34 1 ), if x ≠1 x−1 . Then which one of the following is true?
Q73.If A, B and C are three sets such that A ∩B = A ∩C and A ∪B = A ∪C , then (1) A = B (2) A = C (3) B = C (4) A ∩B = ϕ
Q77.For real x, let f(x) = x3 + 5x + 1, then (1) f is one-one but not onto R (2) f is onto R but not one-one (3) f is one-one and onto R (4) f is neither one-one nor onto R