ISC Class 12th Mathematics Chapter 1 - Relations and Functions Important Questions with Answers

Solve the differential equation  `dy/dx = (x + y+2)/(2(x+y)-1)`

The index number by the method of aggregates for the year 2010, taking 2000 as the base year, was found to be 116. If sum of the prices in the year 2000 is ? 300, find the values of x and y in the data given below

If the function f : R ? R be defined by f(x) = 2x ? 3 and g : R ? R by g(x) = x³ + 5, then find the value of (fog)^?1 (x).

Let f : W ? W be defined as

`f(n)={(n-1, " if n is odd"),(n+1, "if n is even") :}`

Show that f is invertible a nd find the inverse of f. Here, W is the set of all whole
numbers.

The binary operation *: R x R ? R is defined as a *b = 2a + b Find (2 * 3)*4

Solve `3tan^(-1)x + cot^(-1) x = pi`

If the function `f(x) = sqrt(2x - 3)` is invertible then find its inverse. Hence prove that `(fof^(-1))(x) = x`

if `tan^(-1) a + tan^(-1) b + tan^(-1) x = pi`, prove that a + b + c = abc 

Let \[f\left(x\right) = x^3\] be a function with domain {0, 1, 2, 3}. Then domain of \[f^{-1}\] is ______.

Solve:  sin(2 tan ^-1 x)=1