Operations with Functions and Composition of Functions

Front

What is the sum of two functions f(x) and g(x)?

Back

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

Front

How do you find the composition of two functions g(h(x))?

Back

Substitute h(x) into g(x).

Front

What is the definition of function composition?

Back

Function composition is the application of one function to the results of another, denoted as (f ∘ g)(x) = f(g(x)).

Front

What is the difference between two functions f(x) and g(x)?

Back

(f - g)(x) = f(x) - g(x).

Front

What is the product of two functions f(x) and g(x)?

Back

(f * g)(x) = f(x) * g(x).

Front

If 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

If g(x) = 3x + 4 and h(x) = 3x - 1, find g(h(x)).

Back

g(h(x)) = 9x + 1.

Front

If f(x) = 2x and g(x) = x^2 + 3, find f(g(x)).

Back

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

Front

If f(x) = x^2 + 9 and g(x) = x - 9, find f(x) - g(x).

Back

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

Front

If f(x) = 4x + 1 and g(x) = 4x - 3, find f(x) * g(x).

Back

f(x) * g(x) = 16x^2 - 8x - 3.