Question

Given the parent function f(x)=ln(x),

(a) Write a function whose graph has been reflected in the x-axis, is three times as tall, and has been shifted four units to the left.

(b) Write a function whose graph has been reflected in the y-axis, has been shifted seven units up, and is half as wide.

(c) Calculate the inverse function for your answer to question (b).

Answer 1

Explanation:

(a) The function whose graph has been reflected in the x-axis, is three times as tall, and has been shifted four units to the left is f(x) = -3ln(x+4).

(b) The function whose graph has been reflected in the y-axis, has been shifted seven units up, and is half as wide is f(x) = 1/2(7-ln(x)).

(c) To find the inverse function of f(x) = 1/2(7-ln(x)), we need to solve for x in terms of y. We can do this by first subtracting 7 from both sides of the equation, then multiplying both sides by 2, to get 2y-7 = -ln(x). We can then exponentiate both sides of the equation to get e^(2y-7) = x. This means that the inverse function is f^(-1)(x) = e^(2y-7).