For the given functions find f o gx and g o fx and the domai

For the given functions, find (f o g)(x) and (g o f)(x) and the domain of each. f(x)=7x + 1, g(x) = Squarerootx (g o f)(x) = The domain of f o g is The dom-iin of g o f is (Type an integer or a fraction.)

Solution

f(x) = 7x + 1 ; g (x) = x

Then fog(x) = f ( g(x) ) = f (x) = ( 7x ) + 1 and gof (x) = g ( f (x) ) = g ( 7x + 1) = (7x + 1)

The domain of a function is the set of all possible x values for the function.

The domain of fog (x) = ( 7x ) + 1 is { x R: x 0}

The domain of gof (x) = (7x + 1) is { x R: x - 1/7}