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

Front

How do you find (f - g)(x)?

Back

To find (f - g)(x), subtract the output of g(x) from f(x): (f - g)(x) = f(x) - g(x).

Front

What is the formula for function multiplication?

Back

Function multiplication is defined as (f * g)(x) = f(x) * g(x).

Front

Define function division.

Back

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

Front

What is the composition of functions?

Back

The composition of functions is denoted as (f ∘ g)(x) = f(g(x)). It means applying g first and then applying f to the result.

Front

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

Back

To evaluate f(g(x)), first find g(x) and then substitute that result into f.

Front

What is the result of f(x) = x^2 + 1 and g(x) = 2x - 5 when finding f(x) - g(x)?

Back

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

Front

Given f(x) = 3x^2 + 7x and g(x) = 2x^2 - x - 1, what is (f + g)(x)?

Back

(f + g)(x) = 5x^2 + 6x - 1.

Front

What is the value of (h/j)(-2) if h(x) = x^2 - 3x - 10 and j(x) = 3x - 2?

Back

The value is 0.

Front

How do you find f(g(4)) if f(x) = x^2 + x and g(x) = 3x + 1?

Back

First, calculate g(4) = 3(4) + 1 = 13, then find f(13) = 13^2 + 13 = 182.