F(x)=2x+1/x-1 then f^-1(1)

Mathematics

1 answer:

olasank [31]2 years ago

6 0

Answer:

f⁻¹(x) = (x + 1) / (x - 2)
f⁻¹(1 ) = - 2

Step-by-step explanation:

Given function:

f(x) = (2x + 1) / (x - 1)

Find its inverse, substitute x with y and f(x) with x, solve for y:

x = (2y + 1) / (y - 1)
x(y - 1) = 2y + 1
xy - x = 2y + 1
xy - 2y = x + 1
y(x - 2) = x + 1
y = (x + 1) / (x - 2)

Substitute y with f⁻¹(x):

f⁻¹(x) = (x + 1) / (x - 2)

Find f⁻¹(1 ):

f⁻¹(1 ) = ( 1 + 1) / (1 - 2) = 2 / - 1 = - 2

You might be interested in

Help! Exponential Equation WITHOUT CALCULATOR

ale4655 [162]

$
1.
(2^{x} -2^{-x})^{2} = 4^{2} \\ \\2^{2x}-2*2^{x}*2^{-x} + 2^{-2x} =4^{2} \\ \\2^{2x}-2*2^{x-x} + 2^{-2x} =4^{2} \\ \\ 2^{2x}+ 2^{-2x} - 2=16 \\ \\ 2^{2x}+ 2^{-2x} = 18

\\ \\ 2.( 2^{x})^{3} - (2^{-x}^) ^{3}= (2^{x} -2^{-x})(2^{2x}+2^{x}*2^{-x}+2^{-2x})
\\ \\ ( 2^{x})^{3} - (2^{-x}^)^{3}=(2^{x} -2^{-x})(2^{2x}+2^{-2x}+2^{x}*2^{-x})
\\ \\ ( 2^{x})^{3} - (2^{-x}^)^{3}=(2^{x} -2^{-x})(2^{2x}+2^{-2x}+1)
\\ \\ ( 2^{x})^{3} - (2^{-x}^)^{3}=(2^{x} -2^{-x})((2^{2x}+2^{-2x})+1)
$

$\\ \\ ( 2^{x})^{3} - (2^{-x})^{3} =(4)((18)+1)= 76
\\ \\ 2^{3x}-2^{-3x} =76
$

4 0

3 years ago

Roma sherry drove 80 miles from her home town to her parents' town. during her return trip, she was able to increase her speed

mr_godi [17]

Answer: Roma Sherry drove 330 miles from her hometown to Tucson. During her return trip, she was able to increase her speed by 11 mph. If her return trip took 1 hour less time, find her original speed and her speed returning home. : Let s = original speed then (s+11) = return speed : Write a time equation: Time = distance%2Fspeed : Original time = return time + 1 hr 330%2Fs = 330%2F%28%28s%2B11%29%29 + 1 : Multiply equation by s(s+11) and you have: 330(s+11) = 330s + s(s+11) : 330s + 3630 = 330s + s^2 + 11s : 0 = 330s - 330s + s^2 + 11s - 3630 : A quadratic equation: s^2 + 11s - 3630 = 0 Factor this to: (s + 66)(s - 55) = 0 Positive solution s = 55 mph is original speed. : Find the time 330/55 = 6 hr, original time and 330/66 = 5 hrs, faster time; confirms our solution.

7 0

3 years ago

I know this is really easy but my head hurts so yeah

Ronch [10]

It's hard to read could you just right the number

6 0

3 years ago

Read 2 more answers

What is the prime fractorization of 84

Anvisha [2.4K]

84/2 = 42
42/2 = 21
21/3 = 7
7/7 = 1

84 = 2^2 * 3 * 7

8 0