Problem Solving (PS) | Re: The function f is defined as f(x,y) = xy for positive numbers x and y.

The function f is defined as\( f(x, \ y) =xy\) for positive numbers x and y. If\( f(x, \\frac{1}{x} )=f(x, \y)\) , which of the following must be true?

So\(y=\frac{1}{x}\) .
Let x=2, so y=1/2
Substituting in the options

A.\( f(x, \ x)=f(y, \y)………..2^2=(\frac{1}{2})^2\) …….No

B.\( f(x, \\frac{1}{x} )=f(x, \\frac{1}{y})………2*\frac{1}{2}=2*2\) ……..No

C.\( f(x+y, \\frac{1}{x} )=f(x+y, \\frac{1}{y})……..f(\frac{5}{2},\frac{1}{2})=f(\frac{5}{2},2)……….\frac{5}{4}=5\) ….No

D.\( f(x^2, \ y^2)=f(y(x+1), \\frac{1}{(y+1)})………..f(2^2,(\frac{1}{2})^2)=f((\frac{1}{2})(2+1),\frac{1}{(\frac{1}{2})+1}………2^2*(\frac{1}{2})^2=\frac{3}{2}*\frac{2}{3}…….1=1\) ……..Yes

E.\( f(x, \\frac{1}{y})=1……….f(2,2)=1\) …..No
...

Statistics : Posted by chetan2u • on 04 Oct 2023, 01:30 • Replies 1 • Views 215

---