Advanced Algebra Final Exam

Front

What is the definition of an inverse function?

Back

An inverse function reverses the operation of the original function. If f(x) takes an input x and produces an output y, then the inverse function f^-1(y) takes y back to x.

Front

If f(x) = 2x + 3, what is f^-1(x)?

Back

To find the inverse, swap x and y: y = 2x + 3. Solve for x: x = 2y + 3 -> y = (x - 3)/2. Thus, f^-1(x) = (x - 3)/2.

Front

What points does f^-1(x) go through if f(x) goes through (1, 4) and (4, 6)?

Back

f^-1(x) goes through (4, 1) and (6, 4).

Front

What is the relationship between a function and its inverse?

Back

If f and g are inverse functions, then f(g(x)) = x and g(f(x)) = x for all x in the domain.

Front

If f(2) = -1, what is g(-1)?

Back

g(-1) = 2, since g is the inverse of f.

Front

What is the formula for exponential growth?

Back

The formula is n = n₀ * e^kt, where n₀ is the initial amount, k is the growth rate, and t is time.

Front

If a cell doubles every hour, what function represents the number of cells after h hours if starting with 4 cells?

Back

n = 4(2)^h.

Front

What is the definition of a one-to-one function?

Back

A one-to-one function is a function where each output is produced by exactly one input, meaning f(a) = f(b) implies a = b.

Front

How do you find the inverse of a function given in a table?

Back

To find the inverse, swap the input and output values in the table.

Front

What is the graphical representation of an inverse function?

Back

The graph of an inverse function is a reflection of the original function across the line y = x.