a

{a \over k}

f(x)

g(f(x))=kf(x)

a

kf(a)

f(a)

|k|>1

k = 3 (slider from -5 to 5, step 2)
g(x) = (k * x)
f(x) = (3 * sqrt(x + 5)) - 2
a = 10 (slider from -5 to 10, step 0.1)
b: (a * 1 / k)
fa: f(a)
h(x) = g(f(x))
gb: h(b)
c: x = a
A = Intersect(f, c, (10, 9.618950038622252))
B = Intersect(h, c, (10, 28.856850115866756))
C = Point(c)
e = OrthogonalLine(A, yAxis)
h_1 = OrthogonalLine(B, yAxis)
D = Intersect(e, yAxis)
E = Intersect(h_1, yAxis)
i = Segment(A, D)
j = Segment(B, E)
d = Segment(B, C)
F = Intersect(f, i, (10.000000000000007, 9.618950038622254))
l = Segment(F, C)