import numpy as np
import matplotlib.pyplot as plt
def h(x):
return np.exp(x)
def g(x):
return np.log(x)
g_start, g_end = 0.1, 4
h_start, h_end = g(g_start), g(g_end)
numbers = 100
h_x = np.linspace(h_start, h_end, numbers)
g_x = np.linspace(g_start,g_end, numbers)
h_y = h(x1)
g_y = g(x2)
plt.figure(figsize=(6,6))
plt.plot(h_x, h_y)
plt.plot(g_x, g_y)
plt.plot([-2,2],[-2,2], '--')
x0 = 2
plt.text(x0+0.5, g(x0), r'$g(x0)=y$', fontsize=10)
plt.text(x0-1.3, g(x0)-1.5, r'$g(x)<y$', fontsize=10)
plt.text(g(x0+0.5), x0, r'$h(y)=x0$', fontsize=10)
plt.text(g(x0-1.5), x0-0.6, r'$x<h(y)$', fontsize=10)
plt.plot([x0,x0],[-3,g(x0)], '--')
plt.plot([-3,g(x0)],[x0,x0], '--')
plt.plot([x0, g(x0)], [g(x0),x0])
plt.show()
