Composition of Functions

Front

What is the composition of functions?

Back

The composition of functions is a way of combining two functions where the output of one function becomes the input of another. It is denoted as (f ° g)(x) = f(g(x)).

Front

How do you find the sum of two functions?

Back

To find the sum of two functions f(x) and g(x), you add their outputs: (f + g)(x) = f(x) + g(x).

Front

What is the difference of two functions?

Back

The difference of two functions f(x) and g(x) is found by subtracting the output of g from f: (f - g)(x) = f(x) - g(x).

Front

How do you find the product of two functions?

Back

To find the product of two functions f(x) and g(x), you multiply their outputs: (f * g)(x) = f(x) * g(x).

Front

What is the quotient of two functions?

Back

The quotient of two functions f(x) and g(x) is found by dividing the output of f by the output of g: (f / g)(x) = f(x) / g(x), provided g(x) ≠ 0.

Front

If g(x) = 3x + 12 and h(x) = 6x - 3, what is (g/h)(x)?

Back

Front

If f(x) = x - 5 and g(x) = 3x^2 - 1, what is (f ° g)(x)?

Back

(f ° g)(x) = 3x^2 - 6.

Front

What is the formula for finding (f - g)(x) if f(x) = x^2 + 9 and g(x) = x - 9?

Back

(f - g)(x) = x^2 - x + 18.

Front

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

Back

To evaluate f(g(x)), substitute g(x) into f(x).

Front

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

Back

(f + g)(x) = 2x + (x + 3) = 3x + 3.