3, 9, 27, 81, . . . Use inductive reasoning to predict the next term in the sequence.
2 answers:
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Answer:
Both are inverse pairs
Step-by-step explanation:
Question 11
(a) Rename g(x) as y
(b) Solve for x :
(c) Multiply each side by ⅝
(d) Switch x and y
(e) Rename y as the inverse function
(f) Compare with your function
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).
