Let f(x)=√ log 6 / 5 cos x and g(x)=(2015 x( tan π x- sin π x)/2[(x)π+5]-9) is defined for all x in domain of f(x), then g ( x ) will be [Note: [y] denotes greatest integer function and y denotes fraction part function of y.]

Question

Let f(x)=√ log 6 / 5 cos x and g(x)=(2015 x( tan π x- sin π x)/2[(x)π+5]-9) is defined for all x in domain of f(x), then g ( x ) will be [Note: [y] denotes greatest integer function and y denotes fraction part function of y.] (A) even function (B) odd function (C) both even and odd function (D) neither even nor odd function

Tardigrade Admin · Accepted Answer

Domain of f ( x ), log 6 / 5 cos x ≥ 0 ⇒ cos x ≥ 1 ⇒ cos x =1 ⇒ x =0 ⇒ x ∈ I and when x ∈ I , g ( x )=0 ∴ g is both even and odd function

Q. Let $f (x) = lo g_{6/5} cos {x}$ and $g (x) = \frac{2015 x ( t a n π x - s i n π x )}{2 [ \frac{x}{π} + 5 ] - 9}$ is defined for all $x$ in domain of $f (x)$ , then $g (x)$ will be
[Note: [y] denotes greatest integer function and ${y}$ denotes fraction part function of $y$ .]

even function

odd function

both even and odd function

neither even nor odd function

Domain of $f (x), lo g_{6/5} cos {x} \geq 0 \Rightarrow cos {x} \geq 1 \Rightarrow cos {x} = 1$
$\Rightarrow {x} = 0 \Rightarrow x \in I$ and when $x \in I, g (x) = 0$ $∴ g$ is both even and odd function

Q. Let f(x)=log6/5​cos{x}​ and g(x)=2[πx​+5]−92015x(tanπx−sinπx)​ is defined for all x in domain of f(x), then g(x) will be [Note: [y] denotes greatest integer function and {y} denotes fraction part function of y.]