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ddd [48]
2 years ago
11

What’s the inverse of f(x) = -2 + 2/3x

Mathematics
1 answer:
saveliy_v [14]2 years ago
8 0

So the steps to find the inverse are:

  1. Change f(x) to y
  2. Switch the positions of x and y
  3. Solve for y
  4. Change y to f^-1(x)

f(x)=-2+ \frac{2}{3}x\\\\y=-2+ \frac{2}{3}x\\\\x=-2+ \frac{2}{3}y

Now let's solve for y as such:

x=-2+ \frac{2}{3}y \\\\x+2=\frac{2}{3}y\\\\\frac{3}{2} (x+2)=y\\\\\frac{3}{2}x+3=y\\\\\frac{3}{2}x+3=f^{-1}(x)

<u>Your inverse is f^-1(x) = 3/2x + 3</u>

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Divide 4 2/3 &amp; 3 1/3. Simplify the answer and write it as a mixed number.
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Answer:

4 2/3 ÷ 3 1/3= 1 2/5

Step-by-step explanation:

First, you turn the mixed terms into an improper fraction like this

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Then, you do KCF which stands for <u>Keep Change Flip</u> so for this you would do: 14/3 ÷ 10/3 → 14/3 × 3/10

14 × 3 = 42 and 3 × 10= 30

Now being 42/30 this is considered an improper fraction in which you have to transform it into a mixed number like this:

(For this you need to find the greatest common factor)

42/30 →  42 and 30 greatest common factor is 6 because they are divisible and factor of 6.

Now you divide both the denominator and the numerator y 6 like this:

42 ÷ 6= 7

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Now we have 7/5, this is still an improper number so we see how many times 7 can go to 5 which is once. So we have 1 as whole number, now we put the reminder as the numenator of the mix fraction keeping 5 as being the denominator.

Overall, We have our answer 1 2/5

I hope this helps :D  

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