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

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Answer 1 · 2018-03-08T20:56:12

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

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

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

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

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

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

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

How do you find (hog)(x)(hog)(x)(hog)(x) given h(x)=x^2-2h(x)=x2−2h(x)=x^2-2 and g(x)=4x+1g(x)=4x+1g(x)=4x+1?