Answer:
Let [tex]g(x)[/tex] be a horizontally scaled version of [tex]f(x)[/tex] by [tex]2[/tex]
[tex]g(x) = 2x+5[/tex]
Step-by-step explanation:
Given:
[tex]f(x) = x +5[/tex]
Scaling a function [tex]f(x)[/tex] by a scalar [tex]n[/tex] horizontally, is just multiplying [tex]x[/tex] and [tex]n[/tex] or [tex]f(n\cdot x)[/tex]. In your case, we have to note that shrinking is just another specific word for scaling. If we scale [tex]f(x)[/tex] by scalar, [tex]\frac{1}{2}\\[/tex] horizontally ([tex]f(\frac{1}{2}\cdot x)[/tex]), [tex]f[/tex] would flatten or spread out which would be the opposite of shrinking. To truly shrink [tex]f(x)[/tex], we must have a scalar [tex]n[/tex] greater than [tex]1[/tex]. So the scalar [tex]\frac{1}{2}[/tex] must be the opposite and it is [tex]2[/tex].
We let [tex]g(x)[/tex] be the result when we shrink [tex]f(x)[/tex] horizontally by a scalar, [tex]2[/tex].
[tex]g(x) = f(2\cdot x) \\ g(x) = (2\cdot x) +5 \\ g(x) = 2x+5[/tex]
