Question

Which function is a horizontal compression of its parent function f(x)=x^7 by a factor of 4?

Answer 1

Note that what we want is to compress any point (a, b) in the parent function, to (a, b/4).

(a, b) is a point of the graph of the function $f(x)=x^7$, thus we can rewrite the point as:
                                     $(a, a^7)$.

This point is compressed to 

                                   $\displaystyle{ (a, \frac{a^7}{4} )$.

This means that the function we are looking for is $\displaystyle{ t(x)= \frac{x^7}{4}$.

Answer: t(x)=1/4x^7

Answer 2

The answer is r(x) = (4x)^7