Inverse Function Practice

Front

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

Back

The x's and y's are switched.

Front

Determine the inverse for the function: T(x) = 6x - 7

Back

T^{-1}(x) = \frac{x + 7}{6}

Front

If the equation of f(x) goes through (1, 4) and (4, 6), what points does f^{-1}(x) go through?

Back

(4, 1) and (6, 4)

Front

Determine the inverse for the function: Q(x) = \frac{2x - 7}{4}

Back

Q^{-1}(x) = \frac{4x + 7}{2}

Front

Find the inverse of f(x) = 4x

Back

f^{-1}(x) = \frac{x}{4}

Front

What is the general method to find the inverse of a function?

Back

Replace f(x) with y, switch x and y, and solve for y.

Front

What is the inverse of the function f(x) = x^2 for x >= 0?

Back

f^{-1}(x) = \sqrt{x} for x >= 0.

Front

How do you verify if two functions are inverses?

Back

If f(f^{-1}(x)) = x and f^{-1}(f(x)) = x for all x in the domain.

Front

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

Back

f^{-1}(x) = \frac{x - 2}{3}

Front

What is the relationship between the graphs of a function and its inverse?

Back

They are reflections of each other across the line y = x.