# 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 $$t(x)$$.