AP Precalculus: 2.7-2.12 Review

Front

What is the inverse of a function?

Back

The inverse of a function f, denoted as f^{-1}, is a function that reverses the effect of f. If f(x) = y, then f^{-1}(y) = x.

Front

How do you find the inverse of a function graphically?

Back

To find the inverse of a function graphically, reflect the graph of the function over the line y = x.

Front

What is the definition of a logarithm?

Back

A logarithm is the exponent to which a base must be raised to produce a given number. For example, if b^y = x, then log_b(x) = y.

Front

What is the change of base formula for logarithms?

Back

The change of base formula states that log_b(a) = log_k(a) / log_k(b) for any positive k.

Front

What is the composition of functions?

Back

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

Front

What is the domain of a logarithmic function?

Back

The domain of a logarithmic function log_b(x) is x > 0.

Front

What is the range of a logarithmic function?

Back

The range of a logarithmic function log_b(x) is all real numbers.

Front

How do you evaluate log_8(2)?

Back

Using the change of base formula, log_8(2) = log(2) / log(8) = 1/3.

Front

What is the value of g^{-1}(x) if g(x) = log_3(x-4)?

Back

To find g^{-1}(x), set y = log_3(x-4) and solve for x: x = 3^y + 4.

Front

What is the value of f(g(x)) if f(x) = 2x and g(x) = 2x^2 - 1?

Back

f(g(x)) = f(2x^2 - 1) = 2(2x^2 - 1) = 4x^2 - 2.