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

Question

2659 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-09-06T16:36:34

$(h \circ k) (x) = \frac{x - 2}{x}$ $(h@k)(x) = (x-2)/(x)$

$(h \circ k) (x)$ $(h@k)(x)$ is the same as $h (k (x))$ $h(k(x))$

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

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

$h (k (x)) = \frac{2 x - 4}{(2 x - 4) + 4}$ $h(k(x)) = (2x-4)/((2x-4)+4)$

Then, we simplify:

$h (k (x)) = \frac{2 x - 4}{(2 x - 4) + 4}$ $h(k(x)) = (2x-4)/((2x-4)+4)$

$h (k (x)) = \frac{2 x - 4}{2 x - 4 + 4}$ $h(k(x)) = (2x-4)/(2x-4+4)$

$h (k (x)) = \frac{2 x - 4}{2 x}$ $h(k(x)) = (2x-4)/(2x)$

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

$h (k (x)) = \frac{2 x - 4}{2 x}$ $h(k(x)) = (2x-4)/(2x)$

$h (k (x)) = \frac{2 (x - 2)}{2 (x)}$ $h(k(x)) = (2(x-2))/(2(x))$

$h (k (x)) = \frac{x - 2}{x}$ $h(k(x)) = (x-2)/(x)$

This is already simplified.

$(h \circ k) (x) = \frac{x - 2}{x}$ $(h@k)(x) = (x-2)/(x)$

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