Which of the following hold(s) good for the function `f(x)=2x-3x^(2/3)` `AAx in R`?

For the function f(x)=(x^2+b x+c)3^xa n dg(x)=(x^2+b x+c)3^x+3^x(2x+b)dot Which of the following holds goods? If f(x)>0AAx in R =>g(x)>0AAx in R If f(x)>0AAx in R=>g(x) 0AAx in R=>f(x)>0AAx in R If g(x)>0AAx in R =>f(x)<0AAx in R

Prove that the function f(x)=x^3-3x^2+3x-100 is increasing on R .

Prove that the function f(x)=(2x-1)/(3x+4) is increasing for all x R.

Find the domain of the following functions. f(x)=(log_(2)(x+3))/((x^(2)+3x+2))

Let f(x) be a twice differentiable function for all real values of x and satisfies f(1)=1,f(2)=4,f(3)=9. Then which of the following is definitely true? (a). f''(x)=2AAx in (1,3) (b) f''(x)= 5 for some x in (2,3) (c) f''(x)=3AAx in (2,3) (d) f''(x)=2 for some x in (1,3)

f(x)=(x^(4)+2x^(3)-3x^(2)+4x+12)/(x+3) Which of the following functions is equivalent to the functions above for all values of x for which function above for all values of x for which function f is defined?

Let f(x) be a twice differentiable function for all real values of x and satisfies f(1)=1,f(2)=4,f(3)=9. Then which of the following is definitely true? (a) f^('')=2AAx in (1,3) (b) f^('')=f(x)=5forsom ex in (2,3) (c) f^('')=3AAx in (2,3) (d) f^('')=2forsom ex in (1,3)

Let f:R to R be the function defined by f(x)=2x-3, AA x in R. Write f^(-1).

Discuss the surjectivity of the following functions: f: R-> given by f(x)=x^3+2 for all x in Rdot

Show that the function f(x) = x^3– 3x^2 + 6x – 100 is increasing on R