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)).

Tags

CCSS.HSF-BF.A.1C

Front

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

Back

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

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CCSS.HSF.IF.A.2

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.

Tags

CCSS.HSF-BF.A.1C

Front

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

Back

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

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CCSS.HSF.IF.A.2

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.

Tags

CCSS.HSF-BF.A.1C

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.

Tags

CCSS.HSF-BF.A.1C

Front

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

Back

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

Tags

CCSS.HSF.IF.A.2

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.

Tags

CCSS.HSF-BF.A.1C

Front

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

Back

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

Tags

CCSS.HSF.IF.A.2

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.

Tags

CCSS.HSF-BF.A.1C