Compute the difference quotient f x h f xh for the functio

Compute the difference quotient f (x + h) - f (x)/h for the function below f(x) = 4x^2 + x. Solve for x: log_3 (x + 12) - log_3 (x + 4) = 2 and check the solutions. 2^x + 1 = 3^2x+3 Let f be the one-to-one function. Find the inverse function of: f (x) = 2x + 3/x - 1 f (x) = Squareroot 2x - 3 Perform the following transformations of f (x) = log(x); a) Shift 3 units up, b) Shift the result of a) to 2 units right, c) Reflect the result of b) about the x-axis. Let the trigonometric function f be defined as f(x) = 2sin (3x) What is the amplitude?

Solution

b)function quotient = ([4(x+h)² + (x+h)] - [4x² + x])/h

= (8xh + 4h² +h)/h = 8x + 4h + 1

2 a) log₃(x+12) - log₃(x+4) = 2

=>   log₃[(x+12)/(x+4)] = 2

=>   (x+12)/(x+4) = 9

=> x + 12 = 9x + 36

=> x = -3