Let `f(x) = (1-x)^2 sin^2x + 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?

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 ?

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)-ln t)f(t) dt for all x,in(1,oo). Which of the following is true?

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

Let f(x)=(1-x)^2sin^2x+x^2 for all xinR and let g(x)=int_1^x((2(t-1))/(t+1)-Int) f(t)dt for all xin(1,oo) Which of the following is true ?

Let f(x) = (1 - x)^2 sin^2 x + x^2 for all x ∈ R, and let g(x) = ∫((2(t - 1))/(t + 1) - ln t)f(t)dt for t ∈ [1, x] for all x ∈ (1, ∞).Which of the following is true ?

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

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)-ln t)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 exists some x in IR such that 2f(x)+1=2x(1+x) Then

Let f(x)=(1-x)^(2) sin^(2) x+x^(2) for all x in RR , and let g(x)=int_(1)^(x) ((2(t-1))/(t+1)-log t)f(t) dt for all x in (1, oo) . The number of real roots of the equation f(x)=1 in the interval [0, 1] is -