Home
Class 12
MATHS
Consider a function f : [0, pi/2] rarr R...

Consider a function `f : [0, pi/2] rarr R`
given by f(x) = sin x and `g : [0, pi/2] rarr R`
given by g(x) = cos x. Show that f and g are one-one, but f + g is not one-one.

Promotional Banner

Similar Questions

Explore conceptually related problems

Consider the function f:[0,pi/2]rarrR given by f(x)=sinx and g:[0,pi/2]rarrR given by g(x)=cosx . Show that f and g are one-one functions.

Consider the function f:[0,pi/2]rarrR given by f(x)=sinx and g:[0,pi/2]rarrR given by g(x)=cosx . Is f+g one-one?Why?

Prove that the function f: R rarr R given by f(x)=2 x is one-one and onto.

Show that the function f:R rarr R given by f(x)=x^3 is injective.

If f:RrarrR is given by f(x)=3x-1 , g:RrarrR is given by g(x)=2x ,show that fog-gof=1 .

Consider the function f:R rarr R defined by f(x)=|x-1| . Is f(2)=f(0) ,why?

Consider f:RtoR given by f(x)=5x+2 Show that f is one-one.

If the following f:RrarrR is given by f(x)=(x+3)/3 and g:RrarrR is given by g(x)=2x-3 .Is f^(-1)=g

Consider the function f:R rarr R defined by f(x)=|x-1| . Draw the graph of f(x).

Show that if f: A rarr B and g: B rarr C are one-one, then gof : A rarr C is also one-one.