Function Operations and Compositions

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

Define function composition.

Back

Function composition is the process of applying one function to the results of another function. If f and g are functions, then the composition (f ° g)(x) means f(g(x)).

Front

What is the notation for the difference of two functions?

Back

The difference of two functions f and g is denoted as (f - g)(x) = f(x) - g(x).

Front

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

Back

First, find g(-3) and f(-3): g(-3) = 10, f(-3) = 2. Then, (g - f)(-3) = g(-3) - f(-3) = 10 - 2 = 8.

Front

What is the result of q(p(-2)) if p(x) = 3x + 4 and q(x) = 2x^2?

Back

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

Front

What does it mean if a function is undefined at a certain point?

Back

A function is undefined at a certain point if there is no output for that input, often due to division by zero or taking the square root of a negative number.

Front

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

Back

To find (f ° g)(x), substitute g(x) into f: (f ° g)(x) = f(g(x)) = 3(x^2 + 2) - 1 = 3x^2 + 5.

Front

What is the output of f(g(f(3))) if f(x) = x^2 - 3 and g(x) = x - 3?

Back

First, calculate f(3) = 6. Then, g(6) = 3. Finally, f(3) = 6.

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.