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)+x. Then find the function f(x) .

If f(x)=3x-2a n d(gof)^(-1)(x)=x-2, then find the function g(x)dot

Let f(x)=2x-sin x and g(x)=3sqrt(x) . Then

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

Let f be a differential function such that f(x)=f(2-x) and g(x)=f(1 +x) then (1) g(x) is an odd function (2) g(x) is an even function (3) graph of f(x) is symmetrical about the line x= 1 (4) f'(1)=0

Let g(x) be a function defined on [-1,1]dot If the area of the equilateral triangle with two of its vertices at (0,0) a n d (x ,g(x)) is (sqrt(3))/4 , then the function g(x) is (b) g(x)=+-sqrt(1-x^2) (c) g(x)=sqrt(1-x^2) (d) g(x)=-sqrt(1-x^2) (a) g(x)=sqrt(1+x^2)

If f: RvecR is an odd function such that f(1+x)=1+f(x) and x^2f(1/x)=f(x),x!=0 then find f(x)dot

Find the domain and range of the function f(x)=(1)/sqrt(x-5)

Suppose f(x)=(x+1)^2 for xgeq-1. If g(x) is the function whose graph is the reflection of the graph of f(x) with respect to the line y=x , then g(x) equal. (a) 1-sqrt(x-1),xgeq0 (b) 1/((x+1)^2),x gt-1 (c) sqrt(x+1,)xgeq-1 (d) sqrt(x)-1,xgeq0

Find f'(x) if f(x)=sqrt(x^(2)+1)