Let `f(x)a n dg(x)` be bijective functions where `f:{1, b , c , d}vec{1,2,3,4}a n dg:{3,4,5,6}vec{2, x , y , z},` respectively. Then, find the number of elements in the range of `g"("f(x)"}"dot`

Let f(x) and g(x) be bijective functions where f:{a,b,c,d} to {1,2,3,4} " and " g :{3,4,5,6} to {w,x,y,z}, respectively. Then, find the number of elements in the range set of g(f(x)).

Let L denotes the number of subjective functions f : A -> B, where set A contains 4 elementset B contains 3 elements. M denotes number of elements in the range of the function f(x) = sec^-1(sgmx) + cosec^-1(sgn x) where sg n x denotes signum function of x. And N denotes coefficient of t^5 in (1+t^2)^5(1+t^3)^8. The value of (LM+N) is lambda, then the value of lambda/19 is

For the function f (x) = (x + 3)/( x - 5) to be a bijective function, the domain and range, respectively of f (x) must be :

The equation of the curve is y=f(x)dot The tangents at [1,f(1),[2,f(2)],a n d[3,f(3)] make angles pi/6,pi/3,a n dpi/4, respectively, with the positive direction of x-axis. Then the value of int_2^3f^(prime)(x)f^(x)dx+int_1^3f^(x)dx is equal to (a)-1/(sqrt(3)) (b) 1/(sqrt(3)) (c) 0 (d) none of these

Let f and g be two real values functions defined by f(x)=x+1 and g(x)=2x-3 Find 1)f+g,2 ) f-g,3 ) (f)/(g)

Let f" ":" "N ->R be a function defined as f(x)=4x^2+12 x+15 . Show that f" ":" "N-> S , where, S is the range of f, is invertible. Find the inverse of f.

Which of the following statement is always true? (a)If f(x) is increasing, the f^(-1)(x) is decreasing. (b)If f(x) is increasing, then 1/(f(x)) is also increasing. (c)If fa n dg are positive functions and f is increasing and g is decreasing, then f/g is a decreasing function. (d)If fa n dg are positive functions and f is decreasing and g is increasing, the f/g is a decreasing function.

Let f(x)={x^2-4x+3, ,x<3x-4,xgeq3a n dg(x)={x-3,x<4x^2+2x+2,xgeq4 Describe the function f/g and find its domain.

Let A={0,1,2,3,4,5,6} and f:A rarr N is defined as f(x)=x^(2)+x. Then range of f is

Let f(x) = ([x]+1)/({x}+1) for f: [0, (5)/(2) ) to ((1)/(2) , 3] , where [*] represents the greatest integer function and {*} represents the fractional part of x. Draw the graph of y= f(x) . Prove that y=f(x) is bijective. Also find the range of the function.