Spring 25' AA C&C Flashcard REVIEW-Functions: Composition & Inverses,

Front

What is function composition?

Back

Function composition is the process of applying one function to the results of another function. If you have two functions, f(x) and g(x), the composition is denoted as (f ∘ g)(x) = f(g(x)).

Front

How do you find the inverse of a function?

Back

To find the inverse of a function f(x), you swap the x and y in the equation and solve for y. The inverse is denoted as f^(-1)(x).

Front

What is the composition of the functions a(x) = 4x - 7 and b(x) = (x + 7)/4?

Back

The composition a(b(x)) = a((x + 7)/4) = 4((x + 7)/4) - 7 = x.

Front

What does it mean for a function to be invertible?

Back

A function is invertible if it has a unique output for every input, meaning it passes the horizontal line test.

Front

How do you calculate the inverse of k(x) = 5(x + 6)?

Back

To find the inverse, swap x and y: x = 5(y + 6). Solve for y to get k^(-1)(x) = (x/5) - 6.

Front

What is the formula for compound interest?

Back

The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

Front

What is the value of f^(-1)(-73) if f(x) is invertible and f^(-1)(-73) = -76?

Back

The value of f^(-1)(-73) is -76.

Front

If f(x) is invertible and f^(-1)(-6) = 5, what does this imply?

Back

This implies that f(5) = -6.

Front

What is the interest earned on $250 at 8% compounded quarterly after 7 years?

Back

The interest earned is $185.26.

Front

What is the horizontal line test?

Back

The horizontal line test is a method to determine if a function is one-to-one (invertible). If any horizontal line intersects the graph of the function more than once, the function is not invertible.