# How do you find (hog)(x) given h(x)=x^2-2 and g(x)=4x+1?

Mar 8, 2018

$\left(h \circ g\right) \left(x\right) = 16 {x}^{2} + 8 x - 1$

#### Explanation:

For ease of visualisation set $g \left(x\right) = y = 4 x + 1$

So $h \left(y\right) = {y}^{2} - 2$

but $y = 4 x + 1$ so by substitution we have:

$\left(h \circ g\right) \left(x\right) = {\left(4 x + 1\right)}^{2} - 2$

$\left(h \circ g\right) \left(x\right) = \left(16 {x}^{2} + 8 x + 1\right) - 2$

$\left(h \circ g\right) \left(x\right) = 16 {x}^{2} + 8 x - 1$