Mathematics: Inverse Function Problem?

Question

I need help :(

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Find k if:

f(x)= (x+5)/(x+k)

and if

f(x)= inverse function of f(x)

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I want to know how to solve these kinds of problems.

Thanks!

Answer 1

if

f(x) = (ax+b) / (cx+d)

inverse function of f(x) is;

(-dx + b) / (cx - a)

in your question inverse function of f(x)=(-kx + 5) / (x-1)

if

(-kx + 5) / (x-1) = (x+5) / (x+k);

(x+k) = (x-1) ^ (-kx + 5) = (x+5)

or;

(-kx + 5)*(x+k) = (x-1)*(x+5)

so k=-1

Answer 2

first find the formula for the inverse function

y= (x+5)/(x+k)

make x subject and you'll have your formula.

write x instead of y and make it equal to (x+5)/(x+k)

solve it

Answer 3

x=(y+5)/(y+k)

x(y+k) =y+5

xy +xk =y +5

y(x-1) = -xk +5

y= (-xk +5)/ (x-1)

If f(x) = inverse f(x)

(x+5) / (x+k) =(-xk +5)/(x-1)

and k = -1