One-One, Onto and Bijective Functions

JEE Main Mathematics · Relations and Functions · 9 questions, latest first

• Let f: R → R be defined as f(x)=(2 x^2-3 x+2)/(3 x^2+x+3). Then f is:20266 April, Shift 2 · Q1
• Given below are two statements: Statement I: The function f: R → R defined by f(x)=x/(1+|x|) is one-one. Statement II: The…202628 January, Shift 2 · Q2
• The function f:(-∞, ∞) →(-∞, 1), defined by f(x)=(2^x-2^-x)/(2^x+2^-x) is:202524 January, Shift 2 · Q1
• Let f(x)= {-a, if -a ≤ x ≤ 0; x+a, if 0<x ≤ a} where a>0 and g(x)=(f(|x|)-|f(x)|) / 2. Then the function g:[-a, a] →[-a, a] is20248 April, Shift 2 · Q2
• The function f(x)=(x^2+2 x-15)/(x^2-4 x+9), x ∈ R is20246 April, Shift 1 · Q2
• Let f, g: R → R be defined as: f(x)=|x-1| and g(x)= {e^x, x ≥ 0; x+1, x ≤ 0.} Then the function f(g(x)) is20245 April, Shift 2 · Q2
• Let f: R → R and g: R → R be defined as f(x)= {log_e x, x>0; e^-x, x ≤ 0} and g(x)= {x, x ≥ 0; e^x, x<0}. Then, gof: R → R is:20241 February, Shift 1 · Q14
• The function f: N-{1} → N; defined by f(n)= the highest prime factor of n, is:202427 January, Shift 1 · Q2
• Let f: R → R be a function such that f(x)=(x^2+2 x+1)/(x^2+1). Then202329 January, Shift 1 · Q62