Precalculus Inverse Functions Quiz: 10 Questions with Explanations

A \(\frac{x-8}{2}\)B \(\frac{x+8}{2}\)C \(\frac{1}{2x+8}\)D \(2x-8\)

Swap x and y, then solve: y = (x – 8)/2. The reciprocal is not the inverse.

A Vertical line testB Midpoint testC Slope testD Horizontal line test

A one-to-one function passes the horizontal line test, so each output has one input.

A 3B 10C \(\frac{1}{10}\)D 13

The inverse reverses the pair: f(3) = 10 means f^-1(10) = 3.

A \((-2,-7)\)B \((2,-7)\)C \((7,2)\)D \((-7,2)\)

Inverse graphs swap coordinates: reflection over y = x sends (a, b) to (b, a).

A Yes, it passes the vertical line testB No, y = 4 meets it twiceC Yes, it is symmetricD No, it has no y-intercept

The horizontal line y = 4 hits the graph at two points, so it is not one-to-one.

A \(x^{-3}\)B \(\sqrt[3]{x}\)C \(\frac{1}{x^{3}}\)D \(3x\)

The inverse of cubing is the cube root: cube root of x^3 is x.

A \([2,\infty)\)B \([0,\infty)\)C \((-\infty,2]\)D \((-\infty,\infty)\)

The range of f becomes the domain of f^-1.

A Reflection over the \(y\)-axisB Reflection over the \(x\)-axisC Reflection over \(y=x\)D Rotation about the origin

The graphs of f and f^-1 are mirror images across y = x.

A \(4x-1\)B \(\frac{4}{x-1}\)C \(\frac{x+1}{4}\)D \(4x+1\)

x = (y – 1)/4 gives y = 4x + 1. The sign of the 1 flips when you move it across.

A \(x\neq 0\)B \(x\ge 0\)C \(x\le 4\)D No restriction is needed

Restricting to x >= 0 passes the horizontal line test, with inverse the square root.