03/25: Function Operations

Front

What is function addition?

Back

Function addition is the operation of adding two functions together. If f(x) and g(x) are two functions, then the sum (f + g)(x) = f(x) + g(x).

Front

What is function subtraction?

Back

Function subtraction is the operation of subtracting one function from another. If f(x) and g(x) are two functions, then the difference (f - g)(x) = f(x) - g(x).

Front

What is function multiplication?

Back

Function multiplication is the operation of multiplying two functions together. If f(x) and g(x) are two functions, then the product (f * g)(x) = f(x) * g(x).

Front

What is function division?

Back

Function division is the operation of dividing one function by another. If f(x) and g(x) are two functions, then the quotient (f / g)(x) = f(x) / g(x), provided g(x) ≠ 0.

Front

What is function composition?

Back

Function composition is the operation of applying one function to the result of another function. If f(x) and g(x) are two functions, then the composition (f ∘ g)(x) = f(g(x)).

Front

How do you find (f + g)(x) if f(x) = 2x + 3 and g(x) = x - 5?

Back

(f + g)(x) = (2x + 3) + (x - 5) = 3x - 2.

Front

How do you find (f - g)(x) if f(x) = 4x - 1 and g(x) = 2x + 2?

Back

(f - g)(x) = (4x - 1) - (2x + 2) = 2x - 3.

Front

How do you find (f * g)(x) if f(x) = x + 1 and g(x) = 3x?

Back

(f * g)(x) = (x + 1)(3x) = 3x^2 + 3x.

Front

How do you find (f / g)(x) if f(x) = x^2 and g(x) = x + 1?

Back

(f / g)(x) = x^2 / (x + 1), provided x + 1 ≠ 0.

Front

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

Back

(f ∘ g)(2) = f(g(2)) = f(4) = 4 + 3 = 7.