Function Composition and Operations

Front

What is function composition?

Back

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

Front

What does (f + g)(x) represent?

Back

The expression (f + g)(x) represents the sum of two functions f(x) and g(x). It is calculated by adding the outputs of f and g for a given input x.

Front

How do you find (f + g)(x) if f(x) = 3x^2 + 7x and g(x) = 2x^2 - x - 1?

Back

(f + g)(x) = (3x^2 + 7x) + (2x^2 - x - 1) = 5x^2 + 6x - 1.

Front

What is the value of f(g(4)) if f(x) = x^2 + x and g(x) = 3x + 1?

Back

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

Front

How do you evaluate (f + g)(2) if f(x) = 3x^2 + 1 and g(x) = 4x + 5?

Back

(f + g)(2) = (3(2)^2 + 1) + (4(2) + 5) = 12 + 13 = 25.

Front

What is g(h(x)) if g(x) = 3x + 4 and h(x) = 3x - 1?

Back

g(h(x)) = g(3x - 1) = 3(3x - 1) + 4 = 9x - 3 + 4 = 9x + 1.

Front

How do you find q(p(-2)) if p(x) = 3x + 4 and q(x) = 2x^2?

Back

First, calculate p(-2): p(-2) = 3(-2) + 4 = -2. Then, calculate q(-2): q(-2) = 2(-2)^2 = 8.

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output for each input from its domain.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.