Review - Flashcard #12 Algebra 2

Front

If f(x) = x^2 and g(x) = 3x - 1, find f(g(x)).

Back

f(g(x)) = 9x^2 - 6x + 1.

Front

Find the inverse of f(x) = 10 + 7x.

Back

f^{-1}(x) = \frac{x - 10}{7}.

Front

Given f(x) = -3x + 7 and g(x) = 2x^2 - 8, find f(g(x)).

Back

f(g(x)) = -6x^2 + 31.

Front

If f(x) = x^2 + 9 and g(x) = x - 9, find f(x) - g(x).

Back

f(x) - g(x) = x^2 - x + 18.

Front

Find all zeros for the polynomial function P(x) = x^3 - 3x^2 - 5x + 15.

Back

Zeros: 3, \sqrt{5}, -\sqrt{5}.

Front

What is the definition of a function?

Back

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

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.

Front

How do you find the inverse of a function algebraically?

Back

To find the inverse, swap x and y in the equation and solve for y.

Front

What is the quadratic formula?

Back

The quadratic formula is x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.

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.