If $h (x) = 2 x - 6$ $h(x)=2x-6$ and $h (g (x)) = 2 - 2 x$ $h(g(x))=2-2x$ , find $g (x)$ $g(x)$ ?

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Answer 1 · 2017-01-31T14:16:19

$g (x) = - x + 4$ $g(x)=-x+4$

Let $g (x) = a x + b$ $g(x)=ax+b$ .

As $h (x) = 2 x - 6$ $h(x)=2x-6$

$h (g (x)) = 2 (a x + b) - 6 = 2 a x + 2 b - 6$ $h(g(x))=2(ax+b)-6=2ax+2b-6$

but $h (g (x)) = 2 - 2 x$ $h(g(x))=2-2x$

Therefore, $2 a = - 2$ $2a=-2$ i.e. $a = - 1$ $a=-1$ and $2 b - 6 = 2$ $2b-6=2$ i.e. $b = 4$ $b=4$

Hence, $g (x) = - x + 4$ $g(x)=-x+4$

If h(x)=2x−6h(x)=2x-6 and h(g(x))=2−2xh(g(x))=2-2x, find g(x)g(x)?