import numpy as np
import matplotlib.pyplot as plt
 
a = 9
b = 10
 
# f(x) = log_a(x-b)
x = np.linspace(10.1, 50, 400)
y = np.log(x - b) / np.log(a)
 
# f^-1(x) = b + a^x
x_inv = np.linspace(-2, 3, 400)
y_inv = b + a**x_inv
 
# линия y=x
line = np.linspace(0, 50, 400)
 
plt.figure(figsize=(8,6))
plt.plot(x, y, label=r'$f(x)=\log_{9}(x-10)$', color="blue")
plt.plot(y_inv, x_inv, label=r'$f^{-1}(x)=10+9^x$', color="red")
plt.plot(line, line, '--', color="gray", label="y=x")
 
plt.xlim(0, 50)
plt.ylim(-2, 5)
plt.xlabel("x")
plt.ylabel("y")
plt.title("Функция и её обратная при a=9, b=10")
plt.legend()
plt.grid(True)
plt.show()

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