a

{a \over k}

f(a)=f(g({a \over k}))=f(k{a \over k})

f(x)

f(g(x))=f(kx)

a

{a \over k}

0<|k|<1

{a \over k}

k = 0.6 (slider from -1 to 1, step 0.1)
g(x) = (k * x)
f(x) = (3 * sqrt(x + 5)) - 2
a = 9.6 (slider from 0 to 10, step 0.1)
b: (a * 1 / k)
fa: f(a)
h(x) = f(g(x))
gb: h(b)
c: y = fa
E = Intersect(c, yAxis)
A = Intersect(h, c, (16.000000000000007, 9.462983904725682))
d = OrthogonalLine(A, xAxis)
B = Intersect(d, xAxis)
e = Segment(A, B)
C = Intersect(f, c, (9.600000000000001, 9.46298390472568))
x1 = OrthogonalLine(C, xAxis)
D = Intersect(x1, xAxis)
i = Segment(C, D)
F = Intersect(h, c, (-96, 9.46298390472568))
j = OrthogonalLine(F, xAxis)
G = Intersect(j, xAxis)
l = Segment(F, G)