Function transformation: shrink horizontally Write the formula for $f(x)$, if the graph of $f$ can be obtained from the graph of $y = g(x)$ by shrink horizontally by a factor of $5$ then shift left $3$ units
The equation should be 
$f(x) = g(5(x+3))$ or $g\left(\frac{1}{5}(x+3)\right)$?
I prefer the second answer but my teacher said the correct is the first one? Can anyone explain for me why it is $5$ instead of $\frac{1}{5}$ while we are dealing with horizontal shrinking? 
Thanks a lot

To shrink a function means to make the graph of the function seems narrower. 
For example, consider the function 
$$f(x)=x^2$$
If you want to make the function shrink horizontally by a factor of 2 you would want the function
$$f(2x) = (2x)^2 = 4x^2$$
On the other hand, you would argue that 
$$f\left(\frac{1}{2}x\right) = \left(\frac{1}{2}x\right)^2 = \frac{1}{4}x^2$$
is correct.
If you graph the functions, you would get



Obviously, the function $f(2x) = (2x)^2 = 4x^2$ seems narrower. Similarly, your question is asking you to shrink the function by a factor of five, so it should be $f(5x)$ instead of $f\left(\frac{1}{5}x\right)$.
