Find the inverse of f(x)=(1/3)^x
1 answer:
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Answer:
see the explanation
Step-by-step explanation:
we have triangle ΔABC
step 1
Rotate 90 degrees clockwise ΔABC about point C to obtain ΔA'B'C'
Remember that
A rotation is a rigid transformation
An object and its rotation are the same shape and size, but the figures may be turned in different directions
so
ΔABC and ΔA'B'C' are congruent
ΔABC≅ ΔA'B'C
step 2
Dilate the triangle ΔA'B'C' to obtain triangle ΔEDF
Remember that
A dilation is a non rigid transformation
A dilation produces similar figures
If two figures are similar, then the ratio of its corresponding angles is proportional and its corresponding angles are congruent
Find the scale factor of the dilation
The scale factor is equal to the ratio of corresponding sides
In this problem
Let
z ----> the scale factor
so
Multiply the length sides of triangle ΔA'B'C' by the scale factor z to obtain the length sides of triangle ΔEDF
Note: in this problem the scale factor z is less than 1
That means ----> the dilation is a reduction