Let h(x) = x/(x+4) and k(x)=2x-4, how do you find (hºk)(x) and simplify?

1 Answer
Sep 6, 2015

(h@k)(x) = (x-2)/(x)

Explanation:

(h@k)(x) is the same as h(k(x))

In other words, simplify h(2x-4).

To do this, we plug in 2x-4, or replace every x in h(x) with 2x-4.

h(k(x)) = (2x-4)/((2x-4)+4)

Then, we simplify:

h(k(x)) = (2x-4)/((2x-4)+4)

h(k(x)) = (2x-4)/(2x-4+4)

h(k(x)) = (2x-4)/(2x)

The numerator and denominator have a common factor of 2, so we factor out 2 and cancel.

h(k(x)) = (2x-4)/(2x)

h(k(x)) = (2(x-2))/(2(x))

h(k(x)) = (x-2)/(x)

This is already simplified.

(h@k)(x) = (x-2)/(x)