Inverse square law means `F prop(1)/(r^2)` (T or F)

If the law of gravitation, insted of being inverse-square law, becomes an inverse cube law.

Let g be the inverse function of f and f'(x)=(x^(10))/(1+x^(2)). If g(2)=a then g'(2) is equal to

Consider f : R_+rarr [4, oo) given by f (x) = x^2 + 4 Show that f is invertible with the inverse f ^–1,of f given by f ^–1(y) = sqrt(y - 4) , where R_+ is the set of all non-negative real numbers.

For the reaction AB_(2)(g)hArrAB(g)+B(g) If prop is negligiable w.r.t 1 then degree of dissociaation (prop) of AB_(2) is proportional to :

Let f be a real-valued function defined on the inverval (-1,1) such that e^(-x)f(x)=2+int_0^xsqrt(t^4+1)dt , for all, x in (-1,1)and f^(-1) be the inverse function of fdot Then (f^(-1))^'(2) is equal to

Let f(x) =int_0^1|x-t|t dt , then A. f(x) is continuous but not differentiable for all x in R B. f(x) is continuous and differentiable for all x in R C. f(x) is continuous for x in R-{(1)/(2)} and f(x) is differentiable for x in R - {(1)/(4),(1)/(2)} D. None of these

If g is te inverse of a function f and f'(x) = 1/(1+x^5) then g'(x) is equal to

f:(0,infty)rarrR and F(x)=int_(0)^(x)t f(t)dt If F(x^(2))=x^(4)+x^(5),"then" Sigma_(r=1)^(12)f(r^(2)) is equal to S

Let f : R – {4/3}rarrR be a function defined as f (x) = 4x/(3x+4) The inverse of f is the (Map) g : Range f rarr R – {4/ 3} , given by :

Let A =R- {2} and B=R - {1}. If f ArarrB is a function defined by f(x) = (x-1)/(x-2) , show that f is one -one and onto, hence find f^(-1)