Inverses & Composition of Functions

Front

What is the inverse of the function f(x) = x^4 - 2?

Back

The inverse is f^(-1)(x) = ∜(x + 2).

Front

If f(x) = 3x - 9, what is f^(-1)(12)?

Back

f^(-1)(12) = 7.

Front

What is the composition of functions f(x) = ∛(x), g(x) = 2x - 5, and j(x) = |x + 3| that results in C(x) = |∛(2x - 5) + 3|?

Back

The composition is j(f(g(x))).

Front

Are the functions f(x) = 3x + 10 and g(x) = x - 2 inverses of each other?

Back

False.

Front

Find f(g(0)) if f(x) = 3x + 10 and g(x) = x - 2.

Back

f(g(0)) = 4.

Front

What is the definition of an inverse function?

Back

An inverse function reverses the operation of the original function, such that f(f^(-1)(x)) = x.

Front

How do you find the inverse of a function algebraically?

Back

To find the inverse, swap x and y in the equation and solve for y.

Front

What is the composition of functions?

Back

The composition of functions f and g, denoted as (f ∘ g)(x), is defined as f(g(x)).

Front

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

Back

f^(-1)(x) = √x, for x ≥ 0.

Front

What is the domain of the inverse function f^(-1)(x) if f(x) = x^4 - 2?

Back

The domain of f^(-1)(x) is x ≥ -2.