If f(x) = 3x - 1 /2 and f^-1 is the inverse of f, what is the value of f^-1(3)?

Solution:

Given, f(x) = (3x - 1)/2

First replace f(x) with y.

y = (3x - 1)/2

Next replace x with y and y with x.

x = (3y - 1)/2

Solving for y, we get,

2x = 3y - 1

3y = 2x + 1

y = 2x/3 + 1/3

Finally replace y with f^-1 (x).

f^-1 (x) = 2x/3 + 1/3 

Now, f^-1 (3) = 2(3)/3 + 1/3 

= 2 + 1/3 

= 7/3

Verification:

(f ∘ f^-1) (x)= x

(f ∘ f^-1) (x)= f [ f^-1 (x)]

= f [2x/3 + 1/3]

= (3[2x/3 + 1/3] - 1)/2

= (2x + 1 - 1)/2

= 2x/2

= x

Therefore, the inverse function when x = 3 is 7/3.

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If f(x) = 3x - 1 /2 and f^-1 is the inverse of f, what is the value of f^-1(3)?

Summary:

If f(x) = 3x - 1 /2 and f^-1 is the inverse of f, the value of f^-1(3) is 7/3.