Question

type the correct answer in each box. use numerals instead of words. the points (-3,4) and (5,-2) are on the graph of function f. if function g is the inverse of function f, what pair of points are on function g? type the point with the lower x - value first. (\square, \square) and (\square, \square)

Explanation:

Step1: Recall inverse function point rule

For a function \( f \) and its inverse \( g = f^{-1} \), if \( (a,b) \) is on \( f \), then \( (b,a) \) is on \( g \).

Step2: Apply to first point \((-3,4)\)

Given point \((-3,4)\) on \( f \), swap \( x \) and \( y \) for inverse. So the point on \( g \) is \((4, -3)\).

Step3: Apply to second point \((5,-2)\)

Given point \((5,-2)\) on \( f \), swap \( x \) and \( y \) for inverse. So the point on \( g \) is \((-2, 5)\).

Step4: Order by lower x - value

Compare \( x \)-values of \((4, -3)\) and \((-2, 5)\). The \( x \)-value of \((-2, 5)\) is \(-2\) and of \((4, -3)\) is \(4\). So lower \( x \)-value first is \((-2, 5)\) then \((4, -3)\).

Answer:

\((-2, 5)\) and \((4, -3)\)