If u(x)=2x2+3andv(x)=1x, what is the range of(uv)(x)?

1 Answer
Jul 23, 2017

uv(x)=u(v(x))=u(1x)=3x22x2

Range: (,3)

Explanation:

u(x)=2x2+3

v(x)=1x

Whichever notation you prefer:
(uv)(x)=u(v(x))

uv(x)=u(v(x))=u(1x)

u(1x)=2x2+3

u(1x)=3x22x2

The horizontal asymptote of this function is at y=3. So, the range of this function is from (,3)