Find the inverse when f(x)=3x^2-3x-2

The inverse of f(x) is (x) =  ± +

Step-by-step explanation:

To find the inverse of the quadratic function f(x) = ax² + bx + c, you should put it in the vertex form f(x) = a(x - h)² + k, where

∵ f(x) = 3x² - 3x - 2

→ Compare it with the 1st form above to find a and b

∴ a = 3 and b = -3

→ Use the rule of h to find it

∵ h = = =

∴ h =  

→ Substitute x by the value of h in f to find k

∵ k = 3( )² - 3( ) - 2

∴ k =

→ Substitute the values of a, h, and k in the vertex form above

∵ f(x) = 3(x -  )² +

∴ f(x) = 3(x -  )² -

Now let us find the inverse of f(x)

∵ f(x) = y

∴ y = 3(x -  )² -

→ Switch x and y

∵ x = 3(y -  )² -

→ Add to both sides

∴ x + = 3(y - )²

→ Divide both sides by 3

∵ = (y - )²

→ Take √ for both sides

∴ ± = y -

→ Add   to both sides

∴ ± + = y

→ Replace y by (x)

∴ (x) =  ± +

∴ The inverse of f(x) is (x) =  ± +

not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this

answer:

it is general formula that is used to write value to its excet position

a11 a12 a13

a21 a22 a23

it is the example of order 2 by 3 matrix in this

a11 means value occur in 1 st row 1st column

a12 means value occurs in 1st row 2nd column

a13 means value occur in 1st row and 3rd column

a21 means value occurs in 2nd row and 1st column

a22 means value occurs in 2nd row and in 2nd column

a23 means value occurs in 2nd row and in 3rd column