Function questions
503 published questions with worked solutions.
- 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
- 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
- Let f:A B be a function defined by f(x)= 3 x+ x+4. If f is invertible, then
- Let f:R R, g:R R be two functions given by f(x)=2x-3 and g(x)=x^3+5. Then (f g)^ -1 (x) is equal to
- If the function f:R R is such that f(x)=x-[x], where [x] denotes the greatest integer less than or equal to x, then f^ -1 (x) is
- Let f(x)=(ax^2+b)^3, then the function g satisfying f(g(x))=g(f(x)) is given by
- If f:R R is a mapping defined by f(x)=x^3+5, then f^ -1 (x) is equal to
- Let A= x R:x 1 and f:A A be defined as f(x)=x(2-x). Then f^ -1 (x) is
- Let A= x R:x 0, -4 x 4 and f:A R be defined by f(x)= |x| x for x A. Then the range of f is
- If a function f:[2, ) B defined by f(x)=x^2-4x+5 is a bijection, then B=
- Let f:R- n R be a function defined by f(x)= x-m x-n , where m n. Then,
- If f:R R is defined by f(x)=x^2+1, then the values of f^ -1 (17) and f^ -1 (-3) respectively are
- Let f:B C and g:A B be bijections. Then (f g)^ -1 =
- If f(x)= ^2x, g(x)= x and h(x)= ^ -1 x, 0 x 1, then
- If g(x)=1+ x and f(g(x))=3+2 x +x, then f(x) is equal to
- Let f:A B and g:B A be two functions such that f g=I_B. Then,
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