Answer:
What's confusing ??? You literally just put a dot on the number line
Example:
1.3, move 3 units to the right of 1 and place a dot there
First step: Create a common denominator with 1/3
1/3 x 5/5 = 5/15
Second step: Subtract
14/15
-5/15
_____
a: 9/15
1. Draw the points in the coordinate axes, as in the attached picture.
2. AB and CD are parallel, (both are parallel to the x-axis)
3. A is closer to the y axis than D and C is closer to the C closer than B
4. So combining 2 and 3, we conclude that ABCD is a trapezoid.
5. The remaining thing to check is whether the trapezoid is isosceles or not. For this we drop the heights to AB from points C and D,
and see that the distances from the feets of these heights to the points A and B are not equal.
Answer: Trapezoid
Answer:
b) ![f^{-1}(x) = \frac{4x+5}{3}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%20%3D%20%5Cfrac%7B4x%2B5%7D%7B3%7D)
Step-by-step explanation:
b) To find the inverse function, switch the
and
variables and solve for
:
![f(x) = \frac{3x-5}{4}\\y = \frac{3x-5}{4}\\x = \frac{3y-5}{4}\\4x = 3y-5\\4x+5 = 3y\\\frac{4x+5}{3} = y\\f^{-1}(x) = \frac{4x+5}{3}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cfrac%7B3x-5%7D%7B4%7D%5C%5Cy%20%3D%20%5Cfrac%7B3x-5%7D%7B4%7D%5C%5Cx%20%3D%20%5Cfrac%7B3y-5%7D%7B4%7D%5C%5C4x%20%3D%203y-5%5C%5C4x%2B5%20%3D%203y%5C%5C%5Cfrac%7B4x%2B5%7D%7B3%7D%20%3D%20y%5C%5Cf%5E%7B-1%7D%28x%29%20%3D%20%5Cfrac%7B4x%2B5%7D%7B3%7D)
Verify Answer:
![f(1) = \frac{3(1)-5}{4} = -0.5\\f^{-1}(-0.5) = \frac{4(-0.5)+5}{3} = 1](https://tex.z-dn.net/?f=f%281%29%20%3D%20%5Cfrac%7B3%281%29-5%7D%7B4%7D%20%3D%20-0.5%5C%5Cf%5E%7B-1%7D%28-0.5%29%20%3D%20%5Cfrac%7B4%28-0.5%29%2B5%7D%7B3%7D%20%3D%201)