1. Pg. 136 Homework Pg. 136#18 – 28 even, 33, 34 Pg. 140 #102 – 107 #13f(g(x) = g(f(x) = x#14f(g(x) = g(f(x) = x #15f(g(x) = g(f(x) = x #17No, it fails the HLT #19No, it fails the HLT#21Yes, it passes VLT and HLT #23No#25Where they meet on y = x #27Circle r = 2, C(0, 2)#29f -1 (x) = x 2 + 2, x ≥ 0 #30f -1 (x) = (⅓)x + 2#31f -1 (x) = (½)x – (5/2) #32f -1 (x) = x 1/3 #35f -1 (x) = x 2 – 2, x ≥ 0

2. 2.7 Inverse Functions Inverse Relations The point (a, b) is in the relation R if, and only if, (b, a) is in the relation R -1. Graphically, an inverse is a reflection of the original graph over the line y = x. The Domain and Range of an equation will just be swapped for the equation’s inverse. In order for an inverse function to exist, first you must be dealing with a function and that function must pass the VLT and the HLT. Equations and their inverse can be composed together to prove they are inverses of each other. Their result will always be x.

3. 2.7 Inverse Functions Inverse Functions Show that f(x) = will have an inverse function. – Find the inverse function and state its domain and range. – Prove that the two are actually inverses. Show that g(x) = will have an inverse function. – Find the inverse function and state its domain and range. – Prove that the two are actually inverses.

4. 2.7 Inverse Functions Inverse Functions Show that f(x) = will have an inverse function. – Find the inverse function and state its domain and range. – Prove that the two are actually inverses. Show that g(x) = will have an inverse function. – Find the inverse function and state its domain and range. – Prove that the two are actually inverses. Will h(x) = x 3 – 5x have an inverse function?

5. 2.7 Inverse Functions Examples Find the inverse of algebraically. State the domain and range. Prove they are inverses. Graph the original equation and the inverse along with the line y = x to show it has the proper symmetry. Find the inverse of f(x) = -x 3 algebraically. Graph the original equation and the inverse along with the line y = x to show it has the proper symmetry.