Question

Two functions g and f are defined in the figure below. Find the Domain and Range of the composition f°g. write your answers in set notation.

Answer 1

Domain: {0, 3, 6}

Range: {5 }

Step-by-step explanation:

The domain of the composite function is the intersection of the domain of f(x) and G(x).

`D=Df(x)\cap Dg(x)`
`D=\mleft\lbrace0,3,6\mright\rbrace`

The range of the function is now restricted by the domain of the composite function. Therefore, the range is found by evaluating the function at the points in the domain of f(x). Doing this gives

`R=\mleft\lbrace5\mright\rbrace`

Note: we did not include 7 in the domain since the input value 5 is not in the domain of f(g(x)).