Compositions and Operations with Functions

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

What does f(g(x)) represent?

Back

f(g(x)) represents the composition of two functions, where the output of g(x) becomes the input of f.

Front

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

Back

To find f(x) - g(x), subtract the expression of g(x) from f(x) for all values of x.

Front

What is the value of g[h(-2)] if g(x) = x^2 + 3 and h(x) = 2x + 1?

Back

To find g[h(-2)], first calculate h(-2) = 2(-2) + 1 = -3, then g(-3) = (-3)^2 + 3 = 9 + 3 = 12.

Front

What is the result of f(x-2) if f(x) = 2x^2 - 5x + 3?

Back

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

Front

What is the difference between a linear function and a quadratic function?

Back

A linear function has the form f(x) = mx + b, while a quadratic function has the form f(x) = ax^2 + bx + c.

Front

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

Back

First, find g(4) = 4^2 + 3 = 19, then evaluate f(19) = 2(19) = 38.

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.

Front

What does it mean for two functions to be inverses?

Back

Two functions f and g are inverses if f(g(x)) = x and g(f(x)) = x for all x in the domain.