A function `g(x)` is defined as `g(x)=1/4f(2x^2-1)+1/2f(1-x^2)a n df(x)` is an increasing function. Then `g(x)` is increasing in the interval. `(-1,1)` `(-sqrt(2/3),0)uu(sqrt(2/3),oo)` `(-sqrt(2/3),sqrt(2/3))` (d) none of these

A function g(x) is defined as g(x)=1/4f(2x^2-1)+1/2f(1-x^2) and f(x) is an increasing function. Then g(x) is increasing in the interval. (a) (-1,1) (b) (-sqrt(2/3),0)uu(sqrt(2/3),oo) (c) (-sqrt(2/3),sqrt(2/3)) (d) none of these

A function g(x) is defined as g(x)=1/4f(2x^2-1)+1/2f(1-x^2) and f(x) is an increasing function. Then g(x) is increasing in the interval. (a) (-1,1) (b) (-sqrt(2/3),0)uu(sqrt(2/3),oo) (c) (-sqrt(2/3),sqrt(2/3)) (d) none of these

A function g(x) is defined as g(x)=(1)/(4)f(2x^(2)-1)+(1)/(2)f(1-x^(2)) and f(x) is an increasing function.Then g(x) is increasing in the interval.(-1,1)(-sqrt((2)/(3)),0)uu(sqrt((2)/(3)),oo)(-sqrt((2)/(3)),sqrt((2)/(3)))( d) none of these

A function g(x) is defined as g(x) = (1)/(4) f(2x^(2) - 1) + (1)/(2) f(1- x^(2)) and f'(x) is an increasing function. Then g(x) is increasing in the interval

If f and g are two functions defined by f(x)=sqrt(x+1) and g(x)=1/x then find the following functions: 2f-3g

If f and g are two functions defined by f(x)=sqrt(x+1) and g(x)=1/x then find the following functions: 2f^2+sqrt2 g

Suppose that g(x)=1+sqrt(x) and f(g(x))=3+2sqrt(x)+x. Then find the function f(x) .

Suppose that g(x)=1+sqrt(x) and f(g(x))=3+2sqrt(x)+xdot Then find the function f(x)dot

Suppose that g(x)=1+sqrt(x) and f(g(x))=3+2sqrt(x)+xdot Then find the function f(x)dot