If `f"' (x)>0,AA x in R,` then for any two real in shers `x_1 and x_2(x_1!=x_2)`

If f'(x)>0 and f''(x)>0AA x in R, then for any two real numbers x_(1) and x_(2),(x_(1)!=x_(2))

If f(x)gt0 and f"(x)gt0 forallx in R, then for any two real numbers x_1 and x_2,(x_1nex_2)

If f(x)+2f(1-x)=x^(2)+1,AA x in R, then the range of f is :

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

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

f(x)+2f(1-x)=x^(2)+2,AA x in R then f(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...... .

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...... .