Mathematics questions
18011 published questions with worked solutions.
- If D_ 30 is the set of the divisors of 30, for x,y D_ 30 we define x+y= LCM (x,y), x y= GCD (x,y), x'= 30 x and f(x,y,z)=(x+y)...
- If X and Y are two non-empty sets and f:X Y is a function such that f(C)= f(x):x C for C X and f^ -1 (D)= x:f(x) D for D Y, then...
- Let f:N Y be a function defined as f(x)=4x+3, where Y= y N:y=4x+3 for some x N . Then f is invertible and its inverse is
- Suppose f:[-2,2] R is defined by f(x)= cases -1, & -2 x 0 x-1, & 0 x 2 cases , then x [-2,2]:x 0 and f(|x|)=x is equal to
- Let f(x)= ax+b cx+d . Then f f(x)=x provided that
- Let f:[4, ) [4, ) be defined by f(x)=5^ x(x-4) . Then f^ -1 (x) is
- If f(x)= 1-x 1+x (x -1), then f^ -1 (x) equals
- If f(x) satisfies the relation 2f(x)+f(1-x)=x^2 for all real x, then f(x) is
- The graph of the function y=f(x) is symmetrical about the line x=2, then
- If the function f:[1, ) [1, ) is defined by f(x)=2^ x(x-1) , then f^ -1 (x) is
- If a function F is such that F(0)=2, F(1)=3 and F(n+2)=2F(n)-F(n+1) for n 0, then F(5) is equal to
- The inverse of the function y= 10^x-10^ -x 10^x+10^ -x is
- If f:R R is defined by f(x)=|x|, then
- If f:R R is defined by f(x)= x and g:(1, ) R is defined by g(x)= x^2-1 , then g f(x) is
- The function f:C C defined by f(x)= ax+b cx+d for x C, where bd 0, reduces to a constant function if
- If f:R R is defined by f(x)=x^2-6x-14, then f^ -1 (2) equals
- Let a and b be two integers such that 10a+b=5 and P(x)=x^2+ax+b. The integer n such that P(10) P(11)=P(n) is
- Let f:(2,3) (0,1) be defined by f(x)=x-[x], then f^ -1 (x) equals
- If f is a polynomial such that f(x) f ( 1x )=f(x)+f ( 1x ) and f(4)=65, then f(6) is
- If f:R R is defined by f(x)=x^3, then f^ -1 (8) is equal to