Show that f(x)=πx-2 and f-1(x)=(x+2/π) are inverse functions of one another
1 answer:
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Given:
A combined figure of a triangular prism and a cuboid.
To find:
The volume of the finished object assuming it is empty inside.
Solution:
From the given figure it is clear that the dimensions of the cuboid are 6 cm, 8 cm and 5 cm.
So, the volume of the cuboid is:
The volume of the cuboid is 240 cubic cm.
The area of a triangle is:
Thus, the base area of the triangular prism whose base is 8 cm and height 4 cm, is:
The volume of a triangular prism is:
Where, B is the base area and h is the height of the prism.
The base area of the triangular prism is 16 square cm and the height is 5 cm. So, the volume of a triangular prism is:
Now, the volume of the given figure is:
Hence, the volume of the finished object is 320 cubic cm.
For this case we have the following expression:
Applying distributive property to the terms within parentheses we have:
We add similar terms on both sides of equality considering that:
Equal signs are added and the same sign is placed.
Different signs are subtracted and the major sign is placed.
We add 7.5x to both sides of equality:
We subtract 72 from both sides of equality:
We divide between 3 on both sides of equality
ANswer:
Distributive property
Add similar terms
Equality property of the sum
Equality subtraction property
Equality property of the division