1 2 3 Is the function fx so find its inverse SO invertible I

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Is the function f(x) so, find its inverse. SO, invertible? If 2x+3

Solution

(1)f(x) = 2/(2x+3)
swap x and y
y=2/(2x+3)
2x+3=2/y
2x=2/y - 3
divide by 2
x=1/y-3/2
  
putting the value of (x) in the given eqn we get
f^-1 = 1/x - 3/2

so all this is true for all (x)

(2) x=2log(y)+3
x=2logy+3
x/logy - 3/logy = 2
1/logy*(x-3) = 2
2/(x-3) = logy
y=(x-3)/2solve for y
x-3=2ln(y)
divide by 2
(x-3)/2 = ln(y)
So, y= e^(x-3)/2

(3) True

Answer