6. Exponential & Logarithmic Functions

Use the properties of inverses to determine whether ƒ and g are inverses. ƒ(x) = log￬2 x+1, g(x) = 2^x-1

Use the properties of inverses to determine whether ƒ and g are inverses. ƒ(x) = log￬4 (x+3), g(x) = 4^x + 3

Write an equation for the inverse function of each one-to-one function given. ƒ(x) = 3^x

Write an equation for the inverse function of each one-to-one function given. ƒ(x) = (1/3)^x

Find ƒ^-1(x), and give the domain and range. ƒ(x) = e^(x-5)

Write an equation for the inverse function of each one-to-one function given. ƒ(x) = 5^x + 1

Write an equation for the inverse function of each one-to-one function given. ƒ(x) = 4^x+2

Find ƒ^-1(x), and give the domain and range. ƒ(x) = e^x + 10

Find ƒ^-1(x), and give the domain and range. ƒ(x) = e^(x+1) - 4

Find ƒ^-1(x), and give the domain and range. ƒ(x) = 2 ln 3x

Find the error in the following 'proof' that 2 < 1.

Exercises 137–139 will help you prepare for the material covered in the next section.Solve for x: a(x - 2) = b(2x + 3)

Exercises 137–139 will help you prepare for the material covered in the next section.Solve: x(x - 7) = 3.

Exercises 137–139 will help you prepare for the material covered in the next section.Solve: (x + 2)/(4x + 3) = 1/x

n Exercises 92–93, rewrite the equation in terms of base e. Express the answer in terms of a natural logarithm and then round to three decimal places. y = 6.5(0.43)^x