1.1-1.4 Basic Flashcard Review

Front

Given f(x) = 2x + 5 and g(x) = x + 3, find f(g(x)).

Back

f(g(x)) = f(x + 3) = 2(x + 3) + 5 = 2x + 6 + 5 = 2x + 11.

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

Are the blue and red graphs inverse functions?

Back

Yes, two functions are inverses if f(g(x)) = x and g(f(x)) = x.

Front

Are these functions inverses?

Back

Yes, if f(g(x)) = x and g(f(x)) = x, then they are inverse functions.

Front

If the domain of f(x) is x ≥ 4, then the ____ of ____ is y ≥ 4.

Back

The range of f^-1(x) is y ≥ 4.

Front

What is a function?

Back

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

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 does it mean for two functions to be inverses?

Back

Two functions are inverses if their compositions yield the identity function: f(g(x)) = x and g(f(x)) = x.

Front

How do you find the inverse of a function?

Back

To find the inverse of a function, swap the x and y variables and solve for y.

Front

What is the composition of functions?

Back

The composition of functions f and g, denoted f(g(x)), is the application of g first, followed by f.