FNGR 2 | Lesson 5 | Try This! (Inverse Relationships) Solutions

1.  Yes inverses. Both lines are functions (they pass the vertical line test), and \(f(x)\) passes the horizontal line test so the inverse could exist, and they are reflections over the line \(y=x\) ; therefore, they are inverse functions.  We can check with points; for example \((-5, 5)\) is on \(f(x)\) and \((5, -5)\) is on \(g(x)\) . 

2.  Not inverses. Both lines are functions (they pass the vertical line test) so they might be inverses.  However, they do not reflect over the line \(y=x\) and they do not intersect at the line \(y=x\) ; therefore, they are not inverse functions.  We can check with points; for example \((0,5)\) is on \(h(x)\) but \((5,0)\) is not on \(k(x)\) .

3. Yes inverses. Both curves are functions (they pass the vertical line test), and \(t(x)\) passes the horizontal line test so the inverse could exist. Additionally, they are reflections over the line \(y=x\) ; therefore, they are inverse functions.  We can check with points; for example \((2,8)\) is on \(r(x)\) and \((8,2)\) is on \(t(x)\).


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