Inverse functions, graphs and derivatives
1. If the ordered pair (2, 3) is on a function which has an inverse, what ordered pair is on that
inverse?
2. Which pair of graphs represent mutually inverse functions?
A
B
C
D
3. If f(x) = 2x + 6 on the domain interval [1, 4], find the range interval.
4. If g(x) = x/2 – 3 on the domain interval [8, 14], find the range interval.
5. Show that f(x) = 2x + 6 on the domain interval [1, 4]
and g(x) = x/2 – 3 on the domain interval [8, 14] are mutually inverse functions.
6. Given function F(x) = x2 – 2x + 4, where x $ 1, find the derivative function, and show that
function F(x) has an inverse function.
7. Determine the domain for the inverse of function F(x).
8. If G(x) represents the inverse of F(x), determine the value of G(4), by solving F(x) = 4.
9. Use the Chain Rule to determine the slope of the tangent line to the graph of G(x) when x = 4.
10. Given function h(x) = -x3 + 3x + 1, for -1 # x # 1,
a) find the value of h(0.5)
b) find the derivative function, and show that h(x) is increasing on its domain
c) find the slope of the tangent line to h(x) at x = 0.5
d) find the slope of the tangent line to the inverse function at x = h(0.5)