Function Composition

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)).

Front

How do you denote the composition of two functions f and g?

Back

The composition of two functions f and g is denoted as f(g(x)).

Front

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

Back

f(g(3)) = f(3^2) = f(9) = 2(9) + 1 = 19.

Front

What is the result of g(f(2)) if f(x) = x + 1 and g(x) = 3x?

Back

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

Front

If f(x) = x - 4 and g(x) = 5x + 2, what is f(g(1))?

Back

f(g(1)) = f(5(1) + 2) = f(7) = 7 - 4 = 3.

Front

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

Back

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

Front

If f(x) = 3x and g(x) = x - 2, what is g(f(4))?

Back

g(f(4)) = g(3(4)) = g(12) = 12 - 2 = 10.

Front

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

Back

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

Front

If f(x) = x^2 - 1 and g(x) = 4x, what is f(g(2))?

Back

f(g(2)) = f(4(2)) = f(8) = 8^2 - 1 = 63.

Front

What is the composition of g(f(x)) if f(x) = x + 3 and g(x) = x^2?

Back

g(f(x)) = g(x + 3) = (x + 3)^2 = x^2 + 6x + 9.