Let `RR and RR^+` be the sets of real numbers and positive real numbers respectively. If `f:RR^+ to RR` be defined by `f(x)=log_ex`, find (a) range of f (b) `{x:f(x)=1}.`
Also show that, f(xy)=f(x)+f(y).

Let RR and QQ be the set of real numbers and rational numbers respectively and f:RR to RR be defined as follows: f(x) =x^2 Find pre-image of (9).

Let RR and QQ be the sets of real numbers and rational numbers respectively. If a in QQ and f: RR rarr RR is defined by , f(x)={(x " when" x in QQ ),(a-x" when " x notin QQ ):} then show that , (f o f ) (x) = x , for all x in RR

Let t the function f:RR to RR be defined by, f(x)=a^x(a gt0 ,a ne1). Find {x:f(x) =1} Also show that, f(x+y)=f(x).f(y) "for all "x,y in RR.

Let RR be the set of real numbers and f : RR to RR be defined by f(x)=sin x, then the range of f(x) is-

Let t the function f:RR to RR be defined by, f(x)=a^x(a gt0 ,a ne1). Find range of f

Let RR be the set of real numbers and the mapping f: RR rarr RR be defined by f(x)=2x^(2) , then f^(-1) (32)=

Let RR and QQ be the set of real numbers and rational numbers respectively and f:RR to RR be defined as follows: f(x)={:{(5",", "when "x in QQ),(-5","," when " x !in QQ):} Find f(3),f(sqrt(3)),f(3.6),f(pi),f(e) and f(3.36),

Let RR be the set of real numbers and f: RR rarr RR be defined by , f(x) =x^(3) +1 , find f^(-1)(x)

Let RR^(+) be the set of positive real numbers and f: RR rarr RR ^(+) be defined by f(x) =e^(x) . Show that, f is bijective and hence find f^(-1)(x)

Let C be the set of complex numbers and the function f:RR to RR,g:C to C be defined by f(x) =x^2 and g(x)=x^2 state with reason whether f = g or not.