Show that a function `f:R to R` given by `f(x)=3x+5` is a bijective.

Let A = { x:x in R ,(-pi)/(2) lt= xlt= (pi)/(2)} and B = (y:y in R , -1 lt= y lt=1} . Show that the function f : A rarr B given by f(x) = sin x is invertible andc hence find f^(-1) .

Show that a fuction f:RrarrR given by f(x)=ax+b, a, bin R and a!=0 is bijective.

Show that the function f:R to R defined by f(x)=(x)/(x^(2)+1) is neither one-one nor onto.

Show that the function f : R^+toR^+ defined by f (x) =x+1/x is injective, but not surjective .

Show that the function f :R rarr R, given by f(x) = cos x, AA x in R is neither one-one nor onto.

Show that the function f: R rarr R given by f(x) = {{:(1,"if" x gt0),(0, "if" x=0),(-1, "if" x lt 0):} is not one - one

Mark as true (T) or false (F). The function f:RrightarrowR defined by f(x)=sinx is bijective.

Show that the function given by f(x) = e^(2x) is strictly increasing on R.

If the function f:R to R is given by f(x)=(x+3)/(3) and g:R to R is given g(x)=2x-3 , then find (i) fog (ii) gof. Is f^(-1)=g ?

Show that the function f : R rarr R defined as f(x) = x^(2) is neither one-one nor onto.