Answer:
Both are inverse pairs
Step-by-step explanation:
Question 11
[tex]g(x)= 4 + \dfrac{8}{5}x[/tex]
(a) Rename g(x) as y
[tex]y = 4 + \dfrac{8}{5}x[/tex]
(b) Solve for x :
[tex]\dfrac{8}{5}x = y - 4[/tex]
(c) Multiply each side by ⅝
[tex]x = \dfrac{5}{8}(y - 4) = \dfrac{5}{8}y - \dfrac{5}{2}[/tex]
(d) Switch x and y
[tex]y = \dfrac{5}{8}x - \dfrac{5}{2}[/tex]
(e) Rename y as the inverse function
[tex]g^{-1}(x) = \dfrac{5}{8}x - \dfrac{5}{2}[/tex]
(f) Compare with your function
[tex]f(x) = \dfrac{5}{8}x - \dfrac{5}{2}\\\\f(x) = g^{-1}(x)[/tex]
f(x) and g(x) are inverse functions.
The graphs of inverse functions are reflections of each other across the line y = x.
In the first diagram, the graph of ƒ(x) (blue) is the reflection of g(x) (red) about the line y = x (black)
Question 12
h(x)= x - 2
(a) Rename h(x) as y
y = x - 2
(b) Solve for x:
x = y + 2
(c) Switch x and y
y = x + 2
(e) Rename y as the inverse function
h⁻¹(x) = x + 2
(f) Compare with your function
f(x) = x + 2
f(x) = h⁻¹(x)
h(x) and ƒ(x) are inverse functions.
The graph of h(x) (blue) reflects ƒ(x) (red) across the line y = x (black).
