If `f(x) ={1` ,`x in Q and ``f(x)= -1` `, x in R-Q . If ``f(1) + f(2) + f(pi) + f(p) =0 ` , then p cannot be

f(x)=x,x in Q and f(x)=1-x,x in R-Q Then find the value of [f(1)]+|(f(e))]|

If f(x) = px +q, where p and q are integers f (-1) = 1 and f (2) = 13, then p and q are

Let f_(1) (x) and f_(2) (x) be twice differentiable functions where F(x)= f_(1) (x) + f_(2) (x) and G(x) = f_(1)(x) - f_(2)(x), AA x in R, f_(1) (0) = 2 and f_(2)(0)=1. "If" f'_(1)(x) = f_(2) (x) and f'_(2) (x) = f_(1) (x) , AA x in R then the number of solutions of the equation (F(x))^(2) =(9x^(4))/(G(x)) is...... .

Let f_(1) (x) and f_(2) (x) be twice differentiable functions where F(x)= f_(1) (x) + f_(2) (x) and G(x) = f_(1)(x) - f_(2)(x), AA x in R, f_(1) (0) = 2 and f_(2)(0)=1. "If" f'_(1)(x) = f_(2) (x) and f'_(2) (x) = f_(1) (x) , AA x in R then the number of solutions of the equation (F(x))^(2) =(9x^(4))/(G(x)) is...... .

Let f(x)= {(1, x in Q), (0, x in R-Q):} and g(x)= {(1, x in R-Q), (0, x in Q):} , find (f+g)(x) and (fg)(x).

Let f_(1) (x) and f_(2) (x) be twice differentiable functions where F(x)= f_(1) (x) + f_(2) (x) and G(x) = f_(1)(x) - f_(2)(x), AA x in R, f_(1) (0) = 2 and f_(2) (0) = 1. "If" f'_(1)(x) = f_(2) (x) and f'_(2) (x) = f_(1) (x) , AA x in R . then the number of solutions of the equation (F(x))^(2) =(9x^(4))/(G(x)) is...... .

If f,g:R to R are defined f(x) = {(0 if , x in Q),(1 if, x in Q):}, g(x) = {(-1 if , x in Q),(0 if, x !in Q):} then find (fog)(pi)+(gof)(e ) .