Let `f[-2,2]rarrR` be a continuous function such that `f(x)`assumes only irrational values. If `f(sqrt2)=sqrt2`,

Let f:[-2,2]toR be a continuous function such that f(x) assumes only irrational values. If f(sqrt(2))=sqrt(2) then-

Let f(x) be a continuous function defined for 1 le x le 3. If f(x) takes rational values for all x and f(2) = 10, then f(1,5) is equal to

Let f(x) be a continuous and periodic function such that f(x)=f(x+T) for all xepsilonR,Tgt0 .If int_(-2T)^(a+5T)f(x)dx=19(agt0) and int_(0)^(T)f(x)dx=2 , then find the value of int_(0)^(a)f(x)dx .

Let f:RrarrR be a continuous odd function, which vanishes exactly at one point and f(1)=1/2. Suppose that F(x)=int_-1^xf(t)dt for all x in[-1,2] . If lim_(xto1)(F(x))/(G(x))=1/14 , then the value of f(1/2) is

Let f: R->R be a continuous function and f(x)=f(2x) is true AAx in R . If f(1)=3, then the value of int_(-1)^1f(f(x))dx is equal to

Let f(x) be non- negative continuous function such that the area bounded by the curve y=f(x) , x- axis and the ordinates x= (pi)/(4) and x = beta ( beta gt (pi)/(4)) is beta sin beta + (pi)/(4) cos beta + sqrt(2) beta . Then the value of f((pi)/(2)) is-

Let f: R->R be a continuous function and f(x)=f(2x) is true AAx in Rdot If f(1)=3, then the value of int_(-1)^1f(f(x))dx is equal to (a)6 (b) 0 (c) 3f(3) (d) 2f(0)

Let f(x) be a non-negative continuous function such that the area bounded by the curve y=f(x), the x-axis, and the ordinates x=pi/4a n dx=beta>pi/4i sbetasinbeta+pi/4cosbeta+sqrt(2)betadot Then f(pi/2) is (pi/2-sqrt(2)-1) (b) (pi/4+sqrt(2)-1) -pi/2 (c) (1-pi/4+sqrt(2))

Let f,[2,7]rarr[0,oo) be a continuous and differentiable function, Then the value if (f(7)-f(2))((f(7))^2+(f(2))^2+f(2)xf(7))/3 is (where cin(2,7) )

Let f(x) be continuous functions f: RvecR satisfying f(0)=1a n df(2x)-f(x)=xdot Then the value of f(3) is 2 b. 3 c. 4 d. 5