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# 2 questions

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

Jul 19, 2020

#1
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2nd question: i still dont know how to do this https://web2.0calc.com/questions/help_83234

Jul 19, 2020
#2
+21959
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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

Jul 19, 2020
#3
+21959
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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

Jul 19, 2020