4.5 Function Operations

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

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

Back

To find f(g(x)), first evaluate g(x) for a specific value of x, then substitute that result into f(x).

Tags

CCSS.HSF-BF.A.1C

Front

What is the formula for adding two functions?

Back

The sum of two functions f(x) and g(x) is given by (f + g)(x) = f(x) + g(x).

Tags

CCSS.HSF-BF.A.1B

Front

What is the formula for subtracting two functions?

Back

The difference of two functions f(x) and g(x) is given by (f - g)(x) = f(x) - g(x).

Tags

CCSS.HSF-BF.A.1B

Front

What is the formula for multiplying two functions?

Back

The product of two functions f(x) and g(x) is given by (f * g)(x) = f(x) * g(x).

Tags

CCSS.HSF-BF.A.1B

Front

What is the formula for dividing two functions?

Back

The quotient of two functions f(x) and g(x) is given by (f / g)(x) = f(x) / g(x), provided g(x) ≠ 0.

Tags

CCSS.HSF-BF.A.1B

Front

Given f(x) = x^2 + 1 and g(x) = 2x - 5, find (f - g)(x).

Back

(f - g)(x) = x^2 - 2x + 6.

Tags

CCSS.HSF-BF.A.1B

Front

Given f(x) = 3x^2 + 7x and g(x) = 2x^2 - x - 1, find (f + g)(x).

Back

(f + g)(x) = 5x^2 + 6x - 1.

Tags

CCSS.HSF-BF.A.1B

Front

What is the value of f(g(4)) if f(x) = x^2 + x and g(x) = 3x + 1?

Back

f(g(4)) = 182.

Tags

CCSS.HSF-BF.A.1C

Front

If f(x) = 3x + 10 and g(x) = x - 2, what is f(g(5))?

Back

f(g(5)) = 19.

Tags

CCSS.HSF-BF.A.1C