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)).

Front

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

Back

g(f(2)) = g(2(2) + 3) = g(7) = 7 - 1 = 6.

Front

What is the notation for function composition?

Back

The notation for function composition is f(g(x)), which means 'apply g first, then apply f to the result of g.'

Front

If f(x) = x^2 and g(x) = 3x, what is f(g(x))?

Back

f(g(x)) = f(3x) = (3x)^2 = 9x^2.

Front

What is the result of g(h(x)) if g(x) = 3x + 4 and h(x) = 3x - 1?

Back

g(h(x)) = g(3x - 1) = 3(3x - 1) + 4 = 9x - 3 + 4 = 9x + 1.

Front

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

Back

g(f(x)) = g(x - 1) = 2(x - 1) = 2x - 2.

Front

What is the composition of two linear functions?

Back

The composition of two linear functions is also a linear function.

Front

If f(x) = 3x + 10 and g(x) = x - 2, what is g(f(x))?

Back

g(f(x)) = g(3x + 10) = (3x + 10) - 2 = 3x + 8.

Front

What is the domain of a composite function?

Back

The domain of a composite function f(g(x)) is the set of all x in the domain of g such that g(x) is in the domain of f.

Front

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

Back

f(g(2)) = f(2 + 1) = f(3) = 3^2 = 9.