1. Tardigrade
  2. Question
  3. Mathematics
  4. If f: R arrow R is a function satisfying the property f (2 x +3)+ f (2 x +7)=2, x ∈ R, then the period of f ( x ) is

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Q. If $f: R \rightarrow R$ is a function satisfying the property $f (2 x +3)+ f (2 x +7)=2, x \in R$, then the period of $f ( x )$ is

Relations and Functions

Solution:

We have, $f(2 x+3)+f(2 x+7)=2\dots$ (1)
Replace $x$ by $x+1, f(2 x+5)+f(2 x+9)=2 \dots$(2)
Now replace $x$ by $x+2, f(2 x+7)+f(2 x+11)=2\dots$(3)
From $(1)-(3)$, we get $f(2 x+3)-f(2 x+11)=0$
i.e., $f(2 x+3)=f(2 x+11) \Rightarrow T=4$