Find the domain of the composite function f g fx 6x 36 gx

Find the domain of the composite function f g.

f(x) = 6x + 36; g(x) = x + 3

a.

{x I x -3, x -6}

b.

{x I x is any real number}

c.

{x I x 9}

d.

{x I x -9}

Solution

here f(x)=6x+36,g(x)=x+3

fog(x)=f(g(x))

=f(x+3)

=6(x+3)+36

=6x+54

so the domain is any real number x

b is correct