Commerce (English Medium) कक्षा १२ - CBSE Question Bank Solutions for Mathematics

Let f : R → R be a function defined by f(x) `= ("e"^abs"x" - "e"^-"x")/("e"^"x" + "e"^-"x")` then f(x) is

Let g(x) = x² – 4x – 5, then ____________.

Let A = R – {3}, B = R – {1}. Let f : A → B be defined by `"f"("x") = ("x" - 2)/("x" - 3)` Then, ____________.

The mapping f : N → N is given by f(n) = 1 + n², n ∈ N when N is the set of natural numbers is ____________.

The function f : R → R given by f(x) = x³ – 1 is ____________.

Let f : [0, ∞) → [0, 2] be defined by `"f" ("x") = (2"x")/(1 + "x"),` then f is ____________.

If N be the set of all-natural numbers, consider f: N → N such that f(x) = 2x, ∀ x ∈ N, then f is ____________.

Let f : R `->` R be a function defined by f(x) = x³ + 4, then f is ______.

Let f : R → R, g : R → R be two functions such that f(x) = 2x – 3, g(x) = x³ + 5. The function (fog)^-1 (x) is equal to ____________.

The domain of the function `"f"("x") = 1/(sqrt ({"sin x"} + {"sin" ( pi + "x")}))` where {.} denotes fractional part, is

Range of `"f"("x") = sqrt((1 - "cos x") sqrt ((1 - "cos x")sqrt ((1 - "cos x")....infty))`

The value of `"tan"^-1 (1/2) + "tan"^-1 (1/3) + "tan"^-1 (7/8)` is ____________.

Solve for x : `"sin"^-1  2 "x" + sin^-1  3"x" = pi/3`

The value of `"tan"^ -1 (3/4) + "tan"^-1 (1/7)` is ____________.

If `"tan"^-1 ("cot"  theta) = 2theta, "then"  theta` is equal to ____________.

`"cot" (pi/4 - 2  "cot"^-1  3) =` ____________.

`"tan"^-1 1 + "cos"^-1 ((-1)/2) + "sin"^-1 ((-1)/2)`

If `"cot"^-1 (sqrt"cos" alpha) - "tan"^-1 (sqrt"cos" alpha) = "x",` the sinx is equal to ____________.

The value of cot `("cosec"^-1 5/3 + "tan"^-1 2/3)` is ____________.

`"sin" {2  "cos"^-1 ((-3)/5)}` is equal to ____________.