Let `f:R->R in pi'k'` largest natural number for which `f(x)=x^3+2k^2+(k^2+12)x-12` is a bijective function, then `(f(1)+f'^-1(49))/10` is equal to

Let f(x)=x^(2)-2x-1AA x in R , Let f,(-oo,a] to [b,oo) , where 'a' is the largest real number for which f(x) is bijective. The value of (a+b) is equal to

f:R rarr R,f(x)=tan^(-1)(2^(x))+k is an odd function, then k is equal to:

Let f(x)=x^2-2x-1 AA x in R Let f:(-oo, a]->[b, oo) , where a is the largest real number for which f(x) is bijective. If f : R->R , g(x) = f(x) + 3x-1 , then the least value of function y = g(|x|) is

Let f(x)=x^2-2x-1 AA xinR Let f:(-oo, a]->[b, oo) , where a is the largest real number for which f(x) is bijective. If f : R->R , g(x) = f(x) + 3x-1 , then the least value of function y = g(|x|) is

If f is given by f(x)={{:(k^(2)x-k,"if "xge1),(2,"if "xlt1):} is a continuous function on R, then find k .

Let f: R->R be a function given by f(x)=x^2+1. Find: f^(-1){10 , 37}

Let f_(1)(x) = x/(x+1) AA x in R^(+) , se of positive real numbers, For k ge 2 , define f_(k)(x) = f_(k-1)(f_(1)(x)) AA x in R^(+) Then f_(2020)(1/2020) is equal to

Let f :R to R be a function such that f(x) = x^3 + x^2 f' (0) + xf'' (2) , x in R Then f(1) equals:

Show that the function f:R-{3}rarr R-{1} given by f(x)=(x-2)/(x-3) is a bijection.