Function Operations

Front

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

Back

The sum of two functions f(x) and g(x) is defined as (f + g)(x) = f(x) + g(x).

Front

What is the difference of two functions f(t) and g(t)?

Back

The difference of two functions f(t) and g(t) is defined as (f - g)(t) = f(t) - g(t).

Front

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

Back

The product of two functions f(x) and g(x) is defined as (f * g)(x) = f(x) * g(x).

Front

What is the quotient of two functions g(x) and h(x)?

Back

The quotient of two functions g(x) and h(x) is defined as (g / h)(x) = g(x) / h(x), provided h(x) ≠ 0.

Front

If f(x) = 2x + 5 and g(x) = 3x - 9, what is (f + g)(x)?

Back

(f + g)(x) = 5x - 4.

Front

If g(x) = 6x + 8 and h(x) = 2, what is (g / h)(x)?

Back

(g / h)(x) = 3x + 4.

Front

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

Back

(f - g)(t) = -t^2 + 3t + 7.

Front

If g(n) = 2n^2 - 1 and h(n) = n^2 + 3n + 6, what is (g - h)(n)?

Back

(g - h)(n) = n^2 - 3n - 7.

Front

If f(x) = 4x - 6 and g(x) = x + 7, what is (f * g)(x)?

Back

(f * g)(x) = 4x^2 + 22x - 42.

Front

What is the definition of function composition?

Back

Function composition is defined as (f ∘ g)(x) = f(g(x)).