If `f: RvecR ,g(x)=f(x)+3x-1,` then the least value of function `y=g(|x|)` is a. -9/4 b. -5/4 c. -2 d. -1

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

If f: RvecR is given by f(x)=(x^2-4)/(x^2+1) , identify the type of function.

Let f(x) be continuous functions f: RvecR satisfying f(0)=1a n df(2x)-f(x)=xdot Then the value of f(3) is 2 b. 3 c. 4 d. 5

Let f(x) be differentiable for real x such that f^(prime)(x)>0on(-oo,-4), f^(prime)(x) 0on(6,oo), If g(x)=f(10-2x), then the value of g^(prime)(2) is a. 1 b. 2 c. 0 d. 4

The function f: RvecR satisfies f(x^2)dotf^(x)=f^(prime)(x)dotf^(prime)(x^2) for all real xdot Given that f(1)=1 and f^(1)=8 , then the value of f^(prime)(1)+f^(1) is 2 b. 4 c. 6 d. 8

If f(x)=(a x^2+b)^3, then find the function g such that f(g(x))=g(f(x))dot

Suppose f: RvecR^+ be a differentiable function such that 3f(x+y)=f(x)f(y)AAx ,y in R with f(1)=6. Then the value of f(2) is 6 b. 9 c. 12 d. 15

If f(x) is an invertible function and g(x)=2f(x)+5, then the value of g^(-1)(x)i s 2f^(-1)(x)-5 (b) 1/(2f^(-1)(x)+5) 1/2f^(-1)(x)+5 (d) f^(-1)((x-5)/2)

If f(x)=x-4,g(x)=x^(2) and h(x)=3x-5 , show that the function is associative .

If f(x) =(e^x)/(1+e^x), I_1=int(f(-a))^(f(a)) xg(x(1-x)dx, and I_2=int_(f(-a))^(f(a)) g(x(1-x))dx, then the value of (I_2)/(I_1) is (a) -1 (b) -2 (c) 2 (d) 1