Mathematics · 2021
JEE Main · 25 July 2021, Shift 2 · Q79
Consider functions f: A → B and g: B → C(A, B, C ⊆ R ) such that (g ° f)^-1 exists, then:
Consider functions $\displaystyle f: A \rightarrow B$ and $\displaystyle g: B \rightarrow C(A, B, C \subseteq \mathbf{R})$ such that $\displaystyle (g \circ f)^{-1}$ exists, then :
Official answer
(1)
$\displaystyle f$ is one-one and $\displaystyle g$ is onto
More from Relations and Functions
- Let for some α ∈ R, f: R → R be a function satisfying f(x+y)=f(x)+2 y^2+y+α x y for all x, y ∈ R. If f(0)=-1 and f(1)=2, then the value of…2026
- Let the sets A and B denote the domain and range respectively of the function f(x)=1/(√(x -x)), where x denotes the smallest integer greater than or…2023
- Consider two sets A={x ∈ Z:|(|x-3|-3)| ≤ 1} and B={x ∈ R-{1,2}: ((x-2)(x-4))/(x-1) log_e(|x-2|)=0}. Then the number of onto functions f: A → B is…2026
- Let R be a relation on R, given by R={(a, b): 3 a-3 b+√7 is an irrational number }. Then R is2023
- Let f: R-{0} → R be a function such that f(x)-6 f(1/x)=35/(3 x)-5/2. If the lim_x → 0(1/(α x)+f(x))=β; α, β ∈ R, then α+2 β is equal to2025
- If the domain of the function log_5(18 x-x^2-77) is (α, β) and the domain of the function log_(x-1)((2 x^2+3 x-2)/(x^2-3 x-4)) is (γ, δ), then…2025
- Let A={1,2,3,4, …., 10} and B={0,1,2,3,4}. The number of elements in the relation R={(a, b) ∈ A × A: 2(a-b)^2+3(a-b) ∈ B} is ____2023
- The function f:(-∞, ∞) →(-∞, 1), defined by f(x)=(2^x-2^-x)/(2^x+2^-x) is:2025
JEE Main 2021 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.