3rd Mid Six Weeks Exam: Inverses and Operations of Functions

Front

What is the sum of the functions f(x) = 9 - 3x and g(x) = 5x - 7?

Back

(f + g)(x) = 2x + 2.

Front

What is the inverse of the coordinates (1, 2), (3, 8), (-3, 6)?

Back

The inverse is (2, 1), (8, 3), (6, -3).

Front

Given f(x) = 3x^2 - 2x + 1 and g(x) = x - 4, what is (f ⋅ g)(x)?

Back

(f ⋅ g)(x) = 3x^3 - 14x^2 + 9x - 4.

Front

Find the inverse of f(x) = (x + 5)^2 - 3.

Back

f^{-1}(x) = \sqrt{x + 3} - 5.

Front

Given f(x) = x^2 + 5 and g(x) = 2x^3 - 1, find (f / g)(-3).

Back

(f / g)(-3) = -14/55.

Front

What is the definition of an inverse function?

Back

An inverse function reverses the operation of the original function, such that if f(a) = b, then f^{-1}(b) = a.

Front

How do you find the inverse of a function algebraically?

Back

To find the inverse, replace f(x) with y, swap x and y, and solve for y.

Front

What is the composition of functions?

Back

The composition of functions f and g, denoted as (f ∘ g)(x), is defined as f(g(x)).

Front

What is the difference between f(x) + g(x) and f(x) * g(x)?

Back

f(x) + g(x) is the sum of the functions, while f(x) * g(x) is the product of the functions.

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.