function composition

Front

What is function composition?

Back

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

Front

What is the inverse of a function?

Back

The inverse of a function f(x) is a function that reverses the effect of f. 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

How do you find the inverse of a linear function?

Back

To find the inverse of a linear function f(x) = ax + b, swap x and y, then solve for y. The inverse is f^-1(x) = (x - b) / a.

Front

What is the notation for the inverse of a function?

Back

The notation for the inverse of a function f is f^-1.

Front

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

Back

f^-1(x) = (x - 3) / 2.

Front

What is the composition of functions f(x) = x + 1 and g(x) = 2x?

Back

(f ∘ g)(x) = f(g(x)) = f(2x) = 2x + 1.

Front

If f(x) = x² and g(x) = x + 1, what is g(f(2))?

Back

g(f(2)) = g(2²) = g(4) = 4 + 1 = 5.

Front

What is the domain of the function f(x) = 1/x?

Back

The domain of f(x) = 1/x is all real numbers except x = 0.

Front

How do you determine if two functions are inverses?

Back

Two functions f and g are inverses if (f ∘ g)(x) = x and (g ∘ f)(x) = x for all x in the domain.

Front

What is the range of the function f(x) = x²?

Back

The range of f(x) = x² is all real numbers y such that y ≥ 0.