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 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 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 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 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 be the set of real numbers and the functions f: RR to RR and g : RR to RR be defined by f(x ) = x^(2)+2x-3 and g(x ) = x+1 , then the value of x for which f(g(x)) = g(f(x)) is -

Let CC and RR be the sets of complex numbers and real numbers respectively . Show that, the mapping f:CC rarr RR defined by, f(z)=|z| , for all z in CC is niether injective nor surjective.

Let RR be the set of real numbers and f:RR to RR be given by, f(x)=log_ex. Does f define a function ?

Let RR be the set of real numbers . If the functions f:RR rarr RR and g: RR rarr RR be defined by , f(x)=3x+2 and g(x) =x^(2)+1 , then find ( g o f) and (f o g) .

Let RR be the set of real numbers and the mapping f: RR rarr RR and g: RR rarr RR be defined by f(x)=5-x^(2) and g(x) =3x -4 , state which of the following is the value of (f o g) (-1) ?

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