If f : R → R is a function satisfying the property f (2x$$ $$+$$ $$3) $$+$$ f (2x$$ $$+$$ $$7) $$=$$ $$2$$, ∀ x ∈ R, then the period of f (x) is

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Infinity Learn · Accepted Answer

We have,f (2x$$ $$+$$ $$3) $$+$$ f (2x$$ $$+$$ $$7) $$=$$ $$2$$                (1)Replace$$ x by x $$+$$ $$1$$,f $$(2x$$ $$+$$ $$5) $$+$$ f (2x$$ $$+$$ $$9) $$=$$ $$2$$                (2)Now$$ replace x by,x $$+$$ $$2$$, f $$(2x$$ $$+$$ $$7) $$+$$ f (2x$$ $$+$$ $$11) $$=$$ $$2$$     (3)From$$ $$(1) – (3), we getf (2x$$ $$+$$ $$3) – f (2x$$ $$+$$ $$11) $$=$$ $$0i$$.e., f (2x$$ $$+$$ $$3) $$=$$ f (2x$$ $$+$$ $$11) ⇒ T $$=$$ $$4$$

If f : R → R is a function satisfying the property f (2x + 3) + f (2x + 7) = 2, ∀ x ∈ R, then the period of f (x) is

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