Let f: R arrow R be a function defined by f(x)=(2(1-(x25/2))(2+x25))(1/50). If the function g(x)=f(f(f(x)))+f(f(x)), the the greatest integer less than or equal to g(1) is

Question

Let f: R arrow R be a function defined by f(x)=(2(1-(x25/2))(2+x25))(1/50). If the function g(x)=f(f(f(x)))+f(f(x)), the the greatest integer less than or equal to g(1) is  (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

f(x)=[2(1-(x25/2))(2+x25)](1/50) f(x)=[(2-x25)(2+x25)](1/50) =(4-x50)1 / 50 f(f(x))=(4-((4-x50)1 / 50)50)1 / 50=x g(x)=f(f(f(x)))+f(f(x)) =f(x)+x g(1)=f(1)+1=31 / 50+1 [g(1)]=[31 / 50+1]=2

Q. Let f:R→R be a function defined by f(x)=(2(1−2x25​)(2+x25))501​. If the function g(x)=f(f(f(x)))+f(f(x)), the the greatest integer less than or equal to g(1) is ______

f(x)=[2(1−2x25​)(2+x25)]501​ f(x)=[(2−x25)(2+x25)]501​ =(4−x50)1/50 f(f(x))=(4−((4−x50)1/50)50)1/50=x g(x)=f(f(f(x)))+f(f(x)) =f(x)+x g(1)=f(1)+1=31/50+1 [g(1)]=[31/50+1]=2

Q. Let $f : R \to R$ be a function defined by $f (x) = (2 (1 - \frac{x ^{25}}{2}) (2 + x^{25}))^{\frac{1}{50}}$ . If the function $g (x) = f (f (f (x))) + f (f (x))$ , the the greatest integer less than or equal to $g (1)$ is ______