Inverse of function equation - looks simple but challenging

Inverse of function equation - looks simple but challenging

Postby Guest » Mon Nov 29, 2021 5:34 pm

can someone solve for inverse of the following function

f(x) = (5x^2+8)/(x+7)
Guest
 

Re: Inverse of function equation - looks simple but challeng

Postby Guest » Wed Dec 01, 2021 8:21 pm

That's pretty straight forward. It's hard to see why you would call that "challenging" since you don't show what you tried.

We can write [tex]f(x)= y= \frac{5x^2+ 8}{x+ 7}[/tex] and get the inverse function by swapping x and y: [tex]x= \frac{5y^2+ 8}{y+ 7}[/tex] and get to the form [tex]y= f^{-1}(x)[/tex] by solving for y.

[tex]x(y+ 7)= xy+ 7x= 5y^2+ 8[/tex]
[tex]5y^2+ xy+ 7x- 8= 0[/tex]

By the quadratic formula
[tex]y= \frac{-x\pm\sqrt{x^2- 140x+ 160}}{10}[/tex]

Now the problem is that "[tex]\pm[/tex]". The original function may not HAVE an inverse. In that case we would need to separate f into two functions, each one of which would have an inverse.
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