If #u(x) = -2x^2+3 and v(x) = 1/x#, what is the range of# (u * v)(x)#?

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Answer 1 · 2017-07-23T04:48:59

#u@v (x) = u(v(x)) = u(1/x) = (3x^2-2)/x^2#

#"Range: " (-oo,3)#

#u(x) = -2x^2+3#

#v(x) = 1/x#

Whichever notation you prefer:
#(u@v) (x) = u(v(x))#

#u@v (x) = u(v(x)) = u(1/x)#

#u(1/x) = (-2)/x^2 + 3#

# u(1/x) = frac{3x^2-2}{x^2}#

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