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If \(f(x) = \frac{3x+2}{5} \) what is the value of \(\left[f^{-1}(4)\right]^{-1}\)?

Guest Jul 19, 2020

Guest · Answer 1 · 2020-07-19T10:41:56

2nd question: i still dont know how to do this https://web2.0calc.com/questions/help_83234

geno3141 · Answer 2 · 2020-07-19T11:12:54

First question: f(x) = ( 3x + 2 ) / 5 ---> y = ( 3x + 2 ) / 5

To find the inverse function:

Step 1: interchange y and x: x = ( 3y + 2 ) / 5

Step 2: solve for y: 5x = 3y + 2

3y + 2 = 5x

3y = 5x - 2

y = ( 5x -2 ) / 3

Step 3: replace y with f^-1(x): f^-1(x) = ( 5x - 2 ) / 3

Find f^-1(4) ---> f^-1(4) = ( 5·4 - 2 ) / 3 = 18 / 3 = 6

Find [ f^-1(4) ]^-1 = [ 6 ]^-1 = 1/6

geno3141 · Answer 3 · 2020-07-19T11:26:28

Second question:

f(x) = 1.8 in three places:

1) -1 <= x <= 1 ---> y = 2x ---> 1.8 = 2x ---> x = 0.9

2) 1 <= x <=2 ---> y = -x + 3 ---> 1.8 = -x + 3 ---> -1.2 = -x ---> x = 1.2

3) 2 <= x <= 4 ---> y = 2x - 3 ---> 1.8 = 2x - 3 ---> 4.8 = 2x ---> x = 2.4