No idea how to get started on this problem?

[super_chris1234]

Hi

I'm preparing for an aptitiude test and have no idea how to even approach this question

Given that
f(x)=(Px+Q)/(x-3)

a) If f^-1(0)=2 and f^-1(2)=4, determine the values of P and Q?

I have not even the slightest idea on how to approach and solve this question.

Any help is greatly appreciated.

Thanks,

Chris

 

[pappus]

Hi

I'm preparing for an aptitiude test and have no idea how to even approach this question

Given that
f(x)=(Px+Q)/(x-3)

a) If f^-1(0)=2 and f^-1(2)=4, determine the values of P and Q?

I have not even the slightest idea on how to approach and solve this question.

Any help is greatly appreciated.

Thanks,

Chris

1. I assume that \(\displaystyle f^{-1}()\) denotes the inverse of f, not the reciprocal.

2. If so: Let \(\displaystyle T_i()\) denotes a term in one variable which is included in the parantheses.

Then \(\displaystyle f: f(x)=y = T_1(x)\) is the equation of the function f

and \(\displaystyle f^{-1}: f^{-1}(y) = x = T_2(y)\) is the equation of the inverse function of f

That means: (2, 0) and (4, 2) are points on the graph of f.

3. Plug in these coordinates into the equation of f. You'll get 2 equations in p, q:

\(\displaystyle \displaystyle{\left|\begin{array}{rcl}\frac{2P+Q}{2-3}=0 \\ \frac{4P+Q}{4-3} = 2 \end{array}\right.}\)

solve for (p, q).

 

[super_chris1234]

Yes, f^-1 denotes the inverse. Would I now solve it using a systems of equations?

 

[pappus]

Yes, f^-1 denotes the inverse. Would I now solve it using a systems of equations?

Yes. You find this system of equations you have to solve in my previous post.

Simplify the equations (the denominators are 1 or (-1)) and then use any convenient method you know.