If `f :[2,oo)rarr(-oo,4],` where `f(x)=x(4-x)` then find `f^-1(x)`

Let f :[1/2,oo)rarr[3/4,oo), where f(x)=x^2-x+1. Find the inverse of f(x). Hence or otherwise solve the equation, x^2-x+1=1/2+sqrt(x-3/4.

If f:[1, oo) rarr [1, oo) is defined as f(x) = 3^(x(x-2)) then f^(-1)(x) is equal to

If f : [0, oo) rarr [0, oo) and f(x) = (x^(2))/(1+x^(4)) , then f is

Let f:[4,oo)to[4,oo) be defined by f(x)=5^(x^((x-4))) .Then f^(-1)(x) is

f : [0, oo) rArr [0, oo), f(x) = (5x)/(5+x) is

if f:[1,oo)->[2,oo) is given by f(x)=x+1/x then f^-1(x) equals to : a) (x+sqrt(x^2-4))/2 b) x/(1+x^2) c) (x-sqrt(x^2-4))/2 d) 1+sqrt(x^2-4)

Let f:(-oo,2] to (-oo,4] be a function defined by f(x)=4x-x^(2) . Then, f^(-1)(x) is

If f : [0, oo) rarr [2, oo) be defined by f(x) = x^(2) + 2, AA xx in R . Then find f^(-1) .

Consider the function f:(-oo,oo)rarr(-oo,oo) defined by f(x)=(x^2-ax+1)/(x^2+ax+1), 0ltalt2 , and let g(x)=int_0^(e^x) (f\'(t)dt)/(1+t^2) . Which of the following is true? (A) g\'(x) is positive on (-oo,0) and negative on (0,oo) (B) g\'(x) is negative on (-oo,0) and positive on (0,oo) (C) g\'(x) changes sign on both (-oo,0) and (0,oo) (D) g\'(x) does not change sign on (-oo,oo)

The function f : (0, oo) rarr [0, oo), f(x) = (x)/(1+x) is