F.1 Intervention (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, what is f(2)?

Back

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

Front

What is the notation for function composition?

Back

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

Front

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

Back

g(3) = 3^2 - 1 = 9 - 1 = 8.

Front

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

Back

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

Front

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

Back

g(-3) = 3(-3) = -9; f(g(-3)) = f(-9) = 2(-9) - 1 = -18 - 1 = -19.

Front

If h(x) = x^2 + 1, what is h(2)?

Back

h(2) = 2^2 + 1 = 4 + 1 = 5.

Front

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

Back

h(2) = 5; g(5) = 15; f(15) = 2(15) - 1 = 30 - 1 = 29.

Front

If f(x) = 2x - 1, what is f(0)?

Back

f(0) = 2(0) - 1 = 0 - 1 = -1.

Front

What is the composition of f(x) = -3x + 7 and g(x) = 2x^2 - 8?

Back

f(g(x)) = f(2x^2 - 8) = -3(2x^2 - 8) + 7 = -6x^2 + 24 + 7 = -6x^2 + 31.