Practice questions
88551 published questions with worked solutions.
- Which of the following functions from Z to itself are bijections?
- f:R R is defined by f(x)= e^ x^2 -e^ -x^2 e^ x^2 +e^ -x^2 . Then f is
- If f(x)=2^x, then f(0),f(1),f(2), are in
- Let f:R R be a function defined by f(x)= (5x+2). Then, f is
- Let f:(- ,2] (- ,4] be a function defined by f(x)=4x-x^2. Then, f^ -1 (x) is
- f:R R given by f(x)=5-3 x is
- Which of the following functions from A= x:-1 x 1 to itself are bijections?
- If f(x)=x^n, n N and g f(x)=n ,g(x), then g(x) can be
- The inverse of the function f:R (1,3) given by f(x)= e^x-e^ -x e^x+e^ -x +2 is
- If X= 1,2,3,4 , then one-one onto mappings f:X X such that f(1)=1, f(2) 2, f(4) 4 are given by
- Let f:R R be defined by f(x)=3x-4. Then, f^ -1 (x) is
- The function f:R R given by f(x)=x^2+x is
- f(x)=| x| has an inverse if its domain is
- Let f:R R be a function defined by f(x)= e^ |x| -e^ -x e^x+e^ -x . Then,
- Let f(x)=x and g(x)=|x| for all x R. Then the function (x) satisfying (x)-f(x) ^2+ (x)-g(x) ^2=0 is
- Let f:A B and g:B C be two functions such that g f:A C is onto. Then,
- Let A= x,y,z , B= u,v,w and f:A B be defined by f(x)=u, f(y)=v, f(z)=w. Then, f is
- Let f(x) be defined on [-2,2] and be given by f(x)= cases -1, & -2 x 0 x-1, & 0<x 2 cases and g(x)=f(|x|)+|f(x)|. Then g(x) is...
- If the functions f and g are defined by f(x)=3x-4 and g(x)=3x+2 for x R respectively, then g^ -1 (f^ -1 (5))=
- Let f:R R be a function defined by f(x)= x^2-8 x^2+2 . Then f is