Question

The graph of f(x)=|x| is reflected over the y-axis and horizontally compressed by a factor of 1/9. Write a formula for function g(x)

Answer 1

Reflection over the y-axis = change $x\mapsto -x$

Compress by a factor of k = multiply by k

So, in your case, we first change the sign of the argument. Note that this has no effect, because f(x) is symmetric with respect to the y-axis:

$|x|\mapsto |-x| = |x|$

Then, we compress the function, multiplying it by the scaling factor:

$|x| \mapsto g(x)=\dfrac{|x|}{9}$