Home
Class 12
MATHS
Consider the statements : P : There ex...

Consider the statements : P : There exists some x IR such that f(x) + 2x = 2(1+x2) Q : There exists some x IR such that 2f(x) +1 = 2x(1+x) `f(x)=(1-x)^(2) sin^(2) x+x^(2)" "AA x in R` Then (A) both P and Q are true (B) P is true and Q is false (C) P is false and Q is true (D) both P and Q are false.

Promotional Banner

Similar Questions

Explore conceptually related problems

Consider the statements : P : There exists some x IR such that f(x) + 2x = 2(1+x2) Q : There exists some x IR such that 2f(x) +1 = 2x(1+x) Then (A) both P and Q are true (B) P is true and Q is false (C) P is false and Q is true (D) both P and Q are false.

If f(x)+2f(1-x)=x^2+2AA x in R, then f(x) given as

If f(x)+2f(1-x)=x^2+2AA x in R, then f(x) given as

Suppose f'(x) exists for each x and h(x)=f(x)-(f(x))^(2)+(f(x))^(3) AA x in R , then

Let f(x) = (1-x)^(2) sin^(2)x+ x^(2) for all x in IR and let g(x) = int_(1)^(x)((2(t-1))/(t+1)-lnt) f(t) dt for all x in (1,oo) . Which of the following is true ?

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

If f (x) +2 f (1-x) =x ^(2) +2 AA x in R and f (x) is a differentiable function, then the value of f'(8) is

Let f(x) = (1-x)^(2) sin^(2)x+ x^(2) for all x in IR and let g(x) = int_(1)^(x)((2(t-1))/(t+1)-lnt) f(t) dt for all x in (1,oo) . Consider the statements : P : There exists some x in IR such that f(x) + 2x = 2 (1+x^(2)) Q : There exist some x in IR such that 2f(x) + 1 = 2x(1+x) Then

Show that: x p q p x q q q xx-p)(x^2+p x-2q^2) .

Let F:R to R be such that F for all x in R (2^(1+x)+2^(1-x)), F(x) and (3^(x)+3^(-x)) are in A.P., then the minimum value of F(x) is: