Find f o g and g o f fx squareroot x 4 gx x2 f o g g o f

Find f o g and g o f. f(x) = squareroot x + 4, g(x) = x^2 f o g g o f Find the domain of each function and each composite function. (Enter your answers using interval notation.)

Solution

f(x)= sqrt(x+4)    g(x) = x²

a.   (fog)(x) = f(g(x))= f(x²) = sqrt (x²+4)

b.    (gof)(x) = g(f(x))= g(sqrt(x+4)) = x+4

domain of f

The term inside the square root cant be negative

Therefore x+4>=0

              x>=-4

Domain is [-4,infinity)

Domain of g

Here their is no restriction on x

Therefore domain is (-infinity,infinity)

Domain of fog

There are no restriction on the starting function that is g(x) and domain of the result is all real numbers

Therefore domain of fog (-infinity,infinity)

Domain of gof

Domain of starting function is x >=-4   and of result is all real numbers. Therefore domain of gof is [4,infinity)