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3 years ago

Find inverse of f(x)=3x+1

1 answer:

6 0

First, replace f(x) with y.

So we have now:

y = 3x + 1

Next, switch the x and y.

We get:

x = 3y + 1

Finally, solve for y.

3y = x - 1

y = x/3 - 1/3

So, we have f(x) = 3x + 1, and the inverse of this function is:

$\boxed{f^{-1}(x) = \frac{1}{3} x - \frac{1}{3}}\\\\OR\\\\\boxed{f^{-1}(x) = \frac{x-1}{3}}$

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3 years ago

The measure (in inches) of the sides of triangle RIO are equivalent to three consecutive odd integers. The perimeter is 201 inch

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Let
x-------------> first odd integer
x+2---------> second odd integer
x+4---------> third odd integer

we know that
(x)+(x+2)+(x+4)=201--------> 3x+6=201--------> 3x=195-------> x=65

the three sides of triangle RIO are
x=65 in
x+2-----> 65+2-----> 67 in
x+4----> 65+4------> 69 in

then
69²=4761----------> c²
(65²+67²)=8714--------> a²+b²
c² < (a²+b²)---------> the triangle RIO is not obtuse
Is acute angle triangle

statements
1) The triangle is obtuse--------> is false
Is acute angle triangle

2) The triangle is scalene-----> is correct
The three sides measures are diferent

3)The smallest side measures 61 inches--------> is false
The smallest side measures 65 in

4)The largest side measures 69 inches-------> is correct

5) If triangle RIO is dilated of 1/3, then the perimeter of the dilated triangle will be 3 units smaller
If triangle RIO is dilated of 1/3, then news sides are
65/3------> 21.67 in
67/3-------> 22.33 in
69/3------> 23 in

the new perimeter is=21.67+22.33+23------> 67 in
201-67=134 in
therefore
If triangle RIO is dilated of 1/3, then the perimeter of the dilated triangle will be 3 units smaller----------> is false

Because the perimeter of the dilated triangle will be 134 units smaller

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