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SSSSS [86.1K]
2 years ago
10

Finding the inverse of the function x^3+3x+1 is beyond the scope of this course. Nevertheless, you should be able to use your kn

owledge of functions and their inverses as well as your graphing calculator to find the following values of the inverse function.
a. f^-1(1)

b. f^-1(5)

c. f^-1(3)
Mathematics
1 answer:
slega [8]2 years ago
4 0

Step-by-step explanation:

{x}^{3}  + 3x + 1 = 1 =  =  =  >  \\  {x}^{3} + 3x = 0 =  =  =  >  \\  x({x}^{2}  + 3) = 0 \\ x = 0 \: or \\  {x}^{2}  + 3 = 0 =  =  =  >  \\  {x}^{2}  =  - 3 =  =  =  > x 1=   \sqrt{ - 3} \: or \: i \sqrt{3}   \\ x2 =  -  \sqrt{ - 3}  =  =  =  > x2 = -  i \sqrt{3}

{x}^{3}  + 3x + 1 = 5 =  =  =  >  \\  {x}^{3} + 3x - 4 =  =  =  > \\  (x - 1)( {x}^{2}   + x + 4) = 0 =  =  =  >  \\ x - 1 = 0 =  =  > x1 = 1 \\  {x}^{2}  + x + 4 = 0 =  =  =  >  \\ x2 =  - 1 + i \sqrt{3}   \\  x3 =  - 1 - i \sqrt{3}

{x}^{3}  + 3x + 1 = 3 =  =  =  >  \\{ x}^{3}  + 3x - 2 = 0 =  =  =  > x = 0.6

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