Composition of Functions (numerical only)

Front

What is a 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 g(f(x)).

Front

How do you find g(f(x))?

Back

To find g(f(x)), first evaluate f(x) for a given x, then take that result and substitute it into g(x).

Front

Given f(x) = 3x - 2 and g(x) = 4x + 1, find g(f(2)).

Back

g(f(2)) = g(3(2) - 2) = g(4) = 4(4) + 1 = 17.

Front

If f(x) = 2x - 3 and g(x) = x^2 + 1, determine g(f(0)).

Back

g(f(0)) = g(2(0) - 3) = g(-3) = (-3)^2 + 1 = 10.

Front

What is the notation for function composition?

Back

The notation for function composition is (g ∘ f)(x) or g(f(x)).

Front

Given f(x) = 4x + 2 and g(x) = 3x - 1, calculate g(f(3)).

Back

g(f(3)) = g(4(3) + 2) = g(14) = 3(14) - 1 = 41.

Front

If f(x) = 2x and g(x) = 2x^2 - 1, find g(f(-1)).

Back

g(f(-1)) = g(2(-1)) = g(-2) = 2(-2)^2 - 1 = 7.

Front

What is the output of g(f(x)) if f(x) = x + 1 and g(x) = 2x?

Back

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

Front

How do you evaluate f[g(5)]?

Back

To evaluate f[g(5)], first find g(5), then substitute that result into f(x).

Front

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

Back

g(f(2)) = g(2^2) = g(4) = 4 + 3 = 7.