Function questions
503 published questions with worked solutions.
- Let f : R R be a function such that f(x) = ax + 3 x + 4 x. Then f(x) is invertible if
- Let R = set of real numbers and R_c = set of real angles in radian measure. If f : R_c R be a mapping such that f(x) = x, x R_c,...
- Let f : R R such that f(x) = 1 1 + x^2 , x R. Then f is
- Let A = x -1 < x < 1 = B. If f : A B be bijective then a possible definition of f(x) is
- Let f : R R be a mapping such that f(x) = x^2 1 + x^2 . Then f is
- If y is a function of x defined by a^ x+y =a^ x +a^ y where a is a real constant (a>1) then the domain of y(x) is
- If f:(3,4) (0,1) is defined by f(x)=x-[x] where [x] denotes the greatest integer function then f^ -1 (x) is
- f and g are two functions such that (fg)(x) = (gf)(x) for all x. Then f and g may be defined as
- A function f: N Z is defined by f(n)= cases n-1 2 , & when n is odd [2mm] - n2, & when n is even. cases The function f is
- If f:[0, ) [0, ) and f(x)= x x+1 then f is
- If f(x) = x - [x] ,| x| where [ ] is the greatest integer function then f(x) is
- Let f(x) be a continuous even periodic function of period a and f(0) = 0. Then
- A real valued function f(x) satisfies the functional equation f(x-y)=f(x)f(y)-f(a-x)f(a+y) where a is a given constant and...
- If f(x) and g(x) are real functions defined by f(x)= cases 0, & x is rational x, & x is irrational cases and g(x)= cases 0, & x...
- If the real-valued function f(x) = x^3 + 3(a^2 - 1)x + 1 be invertible then the set of possible real values of a is
- If f(a + x) = f(2a) for all x R and a is a positive constant then f(x) is
- If f(x) = 1 + x 1 - x then
- A function y = f(x) is invertible only when
- The domain of definition of the function y(x) given by 2^ x + 2^ y = 2 is
- Let E = 1, 2, 3, 4 and F = 1, 2 . Then the number of onto functions from E to F is
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