Identify the symmetry (if any) in the graphs of the following equations.
$y^2-4x^2=4$

A culture of bacteria has a population of $150$ cells when it is first observed. The population doubles every $12~\(\text{hr}\)$, which means its population is governed by the function $p\(\left\)(t\(\right\))=150\(\cdot{2^{\frac{t}{12}\)}}$, where $t$ is the number of hours after the first observation.

What is the population $4~\(\text{days}\)$ after the first observation?

Taxicab fees A taxicab ride costs \$3.50 plus \$2.50 per mile. Let m be the distance (in miles) from the airport to a hotel. Find and graph the function c(m) that represents the cost of taking a taxi from the airport to the hotel. Also determine how much it will cost if the hotel is 9 miles from the airport.

Inverse of composite functions

c. Explain why if g and h are one-to-one, the inverse of ƒ(x) = g(h(x)) exists.

Inverse of composite functions

b. Let g(x) = x² + 1 and h(x) = √x. Consider the composite function ƒ(x) = g(h(x)). Find ƒ⁻¹ directly and then express it in terms of g⁻¹ and h⁻¹

Composite functions

Let ƒ(x) = x³, g (x) = sin x and h(x) = √x .

Find the domain of ƒ o g.

A culture of bacteria has a population of $150$ cells when it is first observed. The population doubles every $12~\(\text{hr}\)$, which means its population is governed by the function $p\(\left\)(t\(\right\))=150\(\cdot{2^{\frac{t}{12}\)}}$, where $t$ is the number of hours after the first observation.

How long does it take the population to triple in size?