0. Functions

Solve the exponential equation.

$4^{x+7}=16$

Solve the exponential equation.

$100^{x}=10^{x+17}$

Solve the exponential equation.

$81^{x+1}=27^{x+5}$

Solve the exponential equation.

$2\cdot10^{3x}=5000$

Use the graph of ƒ to find ƒ⁻¹ (2),ƒ⁻¹ (9), and ƒ⁻¹ (12) <IMAGE>

Find the inverse of the function ƒ(x) = 2x. Verify that ƒ(ƒ⁻¹(x)) = x and ƒ⁻¹(ƒ(x)) = x .

Sketch the graph of the inverse of ƒ. <IMAGE>

Where do inverses exist? Use analytical and/or graphical methods to determine the largest possible sets of points on which the following functions have an inverse.

ƒ(x) = |2x + 1|