inverse of quadratic log functions Can a Log function with a quadratic have an inverse function? The specific question is to find the inverse of f(x)=log_2(x^2−3x−4) The function already fails the horizontal line test, but apparently there is a function of If x>4, f^(-1)(x) = (3+ sqrt(2^(x+2)+25))/(2) If x<-1, f^(-1)(x) = (3-sqrt(2^(x+2)+25))/(2) I was able to find this by swapping the x and y around, but why does it have an inverse function?

hetjurnar02

hetjurnar02

Open question

2022-08-31

inverse of quadratic log functions
Can a Log function with a quadratic have an inverse function? The specific question is to find the inverse of
f ( x ) = log 2 ( x 2 3 x 4 )
The function already fails the horizontal line test, but apparently there is a function of
If
x > 4 , f 1 ( x ) = 3 + 2 x + 2 + 25 2
If
x < 1 , f 1 ( x ) = 3 2 x + 2 + 25 2
I was able to find this by swapping the x and y around, but why does it have an inverse function?

Answer & Explanation

gypePlealeLertv

gypePlealeLertv

Beginner2022-09-01Added 9 answers

If f ( x ) = log 2 ( x 2 3 x 4 ) = y , x 2 3 x 4 = 2 y
f 1 ( y ) = x = 3 ± 25 + 2 y + 2 2
Tess Pollard

Tess Pollard

Beginner2022-09-02Added 8 answers

log 2 ( x 2 3 x 4 ) = y
2 y = x 2 3 x 4
x 2 3 x 4 2 y = 0
x = 3 ± 25 + 2 y + 2 2

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