Question

Let f(x)=|x-5| and g(x)=1/x

write the given function as as a compostition function using f and g.

H(x)=|(1/x)-5|

Answer 1

Question 20817

Let $f(x) = |x - 5|$ and $g(x) = 1 / x$ write the given function as a composition function using $f$ and $g$. $H(x) = |(1 / x) - 5|$.

Solution.

It is clear that $\frac{1}{x} = g(x)$. Let us consider the composition $f \circ g$. Then $f \circ g(x) = f(g(x)) = f\left(\frac{1}{x}\right) = \left|\left(\frac{1}{x}\right) - 5\right|$. That is $H(x) = f \circ g(x)$.

Answer. $H(x) = f \circ g(x)$.