Practice questions
88551 published questions with worked solutions.
- 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
- If f(x)= x x-1 , x 1, then (f f f)(x) (19 times) is equal to
- If f(0)=1, f(1)=5, f(2)=11, then the equation of the polynomial of degree two is
- The function f satisfies the functional equation 3f(x)+2f ( x+59 x-1 )=10x+30 for all real x 1. The value of f(7) is
- Let [x] denote the greatest integer x. If f(x)=[x] and g(x)=|x|, then the value of f (g ( 85 ) )-g (f (- 85 ) ) is
- Let f:R R:f(x)=x^2 and g:R R:g(x)=x+5, then g f is
- If f(x)= ^2x and the composite function g(f(x))=| x|, then the function g(x) is equal to
- Let the functions f,g,h be defined from R to R such that f(x)=x^2-1, g(x)= x^2+1 and h(x)= cases 0, & x<0 x, & x 0 cases , then h...
- If y=f(x)= x+2 x-1 , then
- If f(x)= ( x), then f(x)f(y)- 12 [f ( x y )+f(xy) ] has the value
- If the function f(x) is defined by f(x)=a+bx and f^r=f f f (repeated r times), then f^r(x) is equal to
- Let f (x+ 1x )=x^2+ 1 x^2 , x 0, then f(x) is equal to
- Which of the following functions is inverse of itself?
- If f(x)=(a-x^n)^ 1/n , where a>0 and n N, then f f(x) is equal to
- If a function f satisfies f f(x) =x+1 for all real values of x and if f(0)= 12, then f(1) is equal to
- If f:R R and g:R R are defined by f(x)=x-3 and g(x)=x^2+1, then the values of x for which g f(x) =10 are
- The values of b and c for which the identity f(x+1)-f(x)=8x+3 is satisfied, where f(x)=bx^2+cx+d, are
- The second degree polynomial f(x) satisfying f(0)=0, f(1)=1 and f'(x)>0 for all x (0,1) is
- The function f:R R is defined by f(x)=3^ -x . Observe the following statements: I. f is one-one; II. f is onto; III. f is a...