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)).

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).

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).

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).

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).

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.

Front

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

Back

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

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.

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.

Front

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

Back

f(g(5)) = 19.