Composition of Functions (2)

Front

What is the composition of functions?

Back

The composition of functions is a process where one function is applied to the result of another function, denoted as (f ∘ g)(x) = f(g(x)).

Front

If f(x) = 2x + 3 and g(x) = x^2, what is (f ∘ g)(2)?

Back

(f ∘ g)(2) = f(g(2)) = f(2^2) = f(4) = 2(4) + 3 = 11.

Front

What is the domain of the function f(x) = 1/(x-3)?

Back

The domain is all real numbers except x = 3, expressed as (-∞, 3) ∪ (3, ∞).

Front

How do you express the interval -5 < x ≤ 2 in interval notation?

Back

(-5, 2].

Front

What is the range of the function f(x) = x^2?

Back

The range is [0, ∞) since x^2 is always non-negative.

Front

If f(x) = 3x - 4, what is f(0)?

Back

f(0) = 3(0) - 4 = -4.

Front

What does it mean for a function to be one-to-one?

Back

A function is one-to-one if it never assigns the same value to two different domain elements.

Front

If g(x) = x + 5, what is g(-3)?

Back

g(-3) = -3 + 5 = 2.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a curve is a function; if any vertical line intersects the curve more than once, it is not a function.

Front

What is the inverse of the function f(x) = 2x + 3?

Back

The inverse is f^(-1)(x) = (x - 3)/2.