`f: RR to RR` given by, `f (x) =x^(2) +5,` for all` x in RR` : then the image set is `[RR` is a set of real number]-

Find the image set of the domain of each of the following functions : g:RR to RR defined by, g(x) = x^2+2, for all x in RR, where RR is the set of real numbers.

Let f : RR to RR be given by f(x) = x+ sqrt(x^(2)) is

Find the image set of the domain of each of the following functions : h:RR^+ to RR defined by h(x) = log_ex, " for all " x in RR^+ where RR^+ is the set of positive real numbers.

Let RR be the set real numbers and f: RR rarr RR be given by f(x) =ax +2 , for all x in RR . If (f o f) =I_(RR) , find the value of a

Discuss the bijectivity of the following mapping : f: RR rarr RR defined by f (x) = ax^(3) +b,x in RR and a ne 0' RR being the set of real numbers

If RR rarrC is defined by f(x)=e^(2ix)" for x in RR then, f is (where C denotes the set of all complex numbers)

If the function f:RR to RR is given by f(x) = x for all x inRR and the function g:RR-{0} to RR is given by g(x)=(1/x), "for all "x in RR-{0}, then find the function f+g and f-g.

Let the function f: RR rarr RR be defined by, f(x)=x^(3)-6 , for all x in RR . Show that, f is bijective. Also find a formula that defines f ^(-1) (x) .

Show that , the function f: RR rarr RR defined by f(x) =x^(3)+x is bijective, here RR is the set of real numbers.

If f:RR to RR satisfies f (x+y) =f (x) + f (y) for all x,y in RR and f(1) =7, then the value of sum _(r=1) ^(n) f(r) is-