if 2f(xy)={f(x)}^y+{f(y)}^x x,y belong to R and f(1)=2 Find summation100r-1 f(r)= - Maths - Relations and Functions

Question

if 2f(xy)={f(x)}^y+{f(y)}^x x,y belong to R and f(1)=2 Find
summation100
r-1​​​ f(r)=?

Neha Sethi · Accepted Answer

Dear student
We have2fxy=fxy+fyx   and f1=2If fxy=fx+fyThen fx=logaxIf fxy=fx-fyThen fx=logaxIf fx+f1x=fx
f1xThen fx=1±xnIf fxy+fyx=2fxyThen fx=ax  for any number a Given : 2fxy=fxy+fyx   Put x=1 and y=x we get2fx=f1x+fx 2fx-fx=f1xgiven f1=2⇒fx=2xSo, fr=2rSo, ∑r=1100fr=∑r=1100 2r
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if 2f(xy)={f(x)}^y+{f(y)}^x x,y belong to R and f(1)=2 . Find summation100 r-1​​​ f(r)=?

if 2f(xy)={f(x)}^y+{f(y)}^x x,y belong to R and f(1)=2 . Find summation¹⁰⁰ _r-1f(r)=?