Inverses & Logs

Front

What does it mean to find the inverse of a function?

Back

The x's and y's are switched.

Front

Find the inverse of f(x)=2x-2.

Back

Front

The exponential function f(x)=2^x and the logarithmic function g(x)=log_2(x) are inverses. Their graphs are reflected over which line?

Back

y=x

Front

What is the domain of log(x)?

Back

(0, ∞)

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.

Front

What is the relationship between exponential and logarithmic functions?

Back

They are inverse functions.

Front

If f(x) = a^x, what is the inverse function?

Back

f^{-1}(x) = log_a(x)

Front

What is the base of the natural logarithm?

Back

e (approximately 2.718) is the base of the natural logarithm.

Front

What is the range of the function log(x)?

Back

(-∞, ∞) is the range of log(x).

Front

What is the value of log_2(8)?

Back

3, because 2^3 = 8.