An even periodic function f: R arrow R with period 4 is such that The value of f ( x ) at x =5.12 (where represents fractional part), is

Question

An even periodic function f: R arrow R with period 4 is such that <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/79a6abf62b3ee931e91d92a04a2a27b7-.png" /> The value of f ( x ) at x =5.12 (where represents fractional part), is (A)  f(7.88)  (B)  f (3.26)  (C)  f (2.12)  (D)  f (5.88)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/cd755563214d7c03f8f06eee967f2f37-.png" /> text At x =5.12 ⇒ f ( x )= x -4 text Now f (5.12)=5.12-4=1.12 ∴ f (5.12) =0.12= f (7.88)

Q. An even periodic function $f : R \to R$ with period 4 is such that

The value of ${f (x)}$ at $x = 5.12$ (where \{\} represents fractional part), is

${f (7.88)}$

${f (3.26)}$

${f (2.12)}$

${f (5.88)}$

$At x = 5.12 \Rightarrow f (x) = x - 4$
$Now f (5.12) = 5.12 - 4 = 1.12$
$∴ {f (5.12)} = 0.12 = {f (7.88)}$

Q. An even periodic function f:R→R with period 4 is such that The value of {f(x)} at x=5.12 (where \{\} represents fractional part), is

{f(7.88)}

{f(3.26)}

{f(2.12)}

{f(5.88)}