# Given g(x) = 5x^2 - 4x and h(x) =sqrt(x - 7) how do you find g(h(x))?

Feb 28, 2016

$5 x - 35 - 4 \sqrt{x - 7}$

#### Explanation:

$g \left(h \left(x\right)\right) = g \left(\sqrt{x - 7}\right)$

Now substitute x = $\sqrt{x - 7} \text{ for x in g(x) }$

hence: $g \left(\sqrt{x - 7}\right) = 5 {\left(\sqrt{x - 7}\right)}^{2} - 4 \left(\sqrt{x - 7}\right)$

now ${\left(\sqrt{x - 7}\right)}^{2} = x - 7$

$\Rightarrow g \left(h \left(x\right)\right) = 5 \left(x - 7\right) - 4 \left(\sqrt{x - 7}\right)$

$= 5 x - 35 - 4 \left(\sqrt{x - 7}\right)$