Let `A={x in R :0lt=xlt=1}dot` If `f: AvecA` is defined by `f(x)={x ,ifx Q1-x ,ifx Q` then prove that `fof(x)=x` for all `x in Adot`

Let A={x in R :0lt=xlt=1}dot If f: AvecA is defined by f(x)={x ,ifx in Q, 1-x ,ifx notin Q then prove that fof(x)=x for all x in Adot

Let A={x in R :0lt=xlt=1}dot If f: A->A is defined by f(x)={(x ,, if x in Q) , (1-x ,, if x!in Q):} then prove that fof(x)=x for all x in Adot

Let A={x in R :-4lt=xlt=4 and x!=0} and f: A->R be defined by f(x)=(|x|)/x . Write the range of fdot

Let A={x in R :-4lt=xlt=4 and x!=0} and f: A->R be defined by f(x)=(|x|)/x . Write the range of fdot

Let R and Q be the sets of real numbers and rational numbers respectively.If a in Q and fR rarr R is defined by,f(x)=x when x in Q,a-x when x not in Q then show that fof (x)=x for all x in R

Is the function f defined by f(x)={(x","ifxle1),(5"," ifx>1):} continuous at x=0

Is the function f defined by f(x)={(x","ifxle1),(5"," ifx>1):} continuous at x=1?

Is the function f defined by f(x)={(x","ifxle1),(5"," ifx>1):} continuous at x=2?

Let A={x in R : x!=0,\ -4lt=xlt=4} and f: A->R be defined by f(x)=(|x|)/x for x in Adot Then \ f is a. {-1, 1} b. (3//4,1] c. [3//4,1] d. (3//4,1)