Composition & Inverse Functions: JEE Questions & Solutions

If the domain of the function f(x)= ^-1 ( 5-x3+2x)+ 1 e(10-x) is (-, ] [,)- then 6( + + +) is equal to

If g(x) = 3x^2 + 2x - 3, f(0) = -3 and 4g(f(x)) = 3x^2 - 32x + 72, then f(g(2)) is equal to:

Let f(x) = x and g(x) = x^4 - 2x^3 + 3x^2 - 2x + 22x^2 - 2x + 1. Then the domain of f g is:

Let f, g: (1,) R be defined as f(x) = 2x + 35x + 2 and g(x) = 2 - 3x1 - x. If the range of the function fog: [2, 4] R is [, ], then 1 - is…

Let f: R - -1/2 R and g: R - -5/2 R be defined as f(x) = 2x + 32x + 1 and g(x) = |x| + 12x + 5. What is the domain of f g?

If f(x) = 4x + 36x - 4, with x 23, and (f f)(x) = g(x), where g: R - 23 R - 23, then (g g g)(4) is equal to:

For some a, b, c N, let f(x) = ax - 3 and g(x) = x^b + c, x R. If (f g)^-1(x) = ( x - 72)^1/3, then (f g)(ac) + (g f)(b) is equal to.

Let f^1(x) = 3x + 22x + 3, x R, R - ( - 32). For n 2, define f^n(x) = f^1 f^n-1(x) and if f^5(x) = ax + bbx + a, (a, b) = 1, then a + b is…

Match List I with List II:

Let for x R f(x) = x + |x|2 for x 0 and f(x) = x2 for x < 0 g(x) = cases x^2 & for x 0, x & for x < 0 cases Then the area bounded by the…

Let f and g be two functions defined by: f(x) = cases x + 1, & x < 0 |x - 1|, & x 0 cases, g(x) = cases x + 1, & x < 0 1, & x 0 cases. Then…

For x R, two real valued functions f(x) and g(x) are such that, g(x) = x + 1 and f g(x) = x + 3 - x. Then f(0) is equal to: