Little Functions Problem...

[MathBaby]

Allo, it's been a while since the last time I've posted in this forum. Recently I've found a little functions question that I think I've forgotten how to do it...

Given that function f(x) = 5x - 36/x, find

f-¹(11)

Find the value of x that can be mapped to itself under the function f.

I was really confused on how to solve it. Hope someone can help me solve this little functions problem

Edit: I think the line "Find the value of x that can be mapped to itself under the function f" is not for this question. Maybe it's for the other questions. Not sure about it...

[VBAhack]

f^-1(x) is the inverse function, meaning you want x = f(y). In this specific case:

y = 5x - 36/x

yx = 5x² - 36

0 = 5x² - yx - 36

Use the quadratic formula to find the values of x in terms of y. There are potentially 2. In the specific case of y = 11, x = 4 or x = -1.8

[Xizeta]

I think you just solved f(11) not the inverse

[TBeck]

I think VBAhack is right:
y = 5x - 36/x

inverse (swap x and y):

x = 5y - 36/y

sub in x = 11

11 = 5y - 36/y
11y = 5y^2 - 36
0 = 5y^2 - 11y -36
y = 4 or y = -1 4/5

[MathBaby]

Yay, the answer is correct

Thank you so much for helping me with this question, I was wondering how they get 4 and -9/5 for answer lol...