Let f be an odd function defined on the real numbers such that f x -3 sin x -4 cos x- for x - 0- then f x for x -0 is A- 3 sin x-4 cos xB- -3 sin x-4 cos xC- -3 sin x-4 cos xD- 3 sin x-4 cos x

The correct option is A 3sin x 4cos xf( x)= f(x) for odd function ⇒ f( x) = (3sin x +4cos x) ⇒ f( x) nbsp;= 3sin x 4cos x nbsp; Replacing x by x, we ge ...

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Standard X

Mathematics

Complementary Trigonometric Ratios

Let f be an o...

Question

Let $f$ be an odd function defined on the real numbers such that $f (x) = 3 sin x + 4 cos x$ , for $x \geq 0$ , then $f (x)$ for $x < 0$ is

3 sin x - 4 cos x

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- 3 sin x + 4 cos x

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- 3 sin x - 4 cos x

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3 sin x + 4 cos x

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Solution

The correct option is A $3 sin x - 4 cos x$
$f (- x) = - f (x)$ for odd function
$\Rightarrow f (- x) = - (3 sin x + 4 cos x) \Rightarrow f (- x) = - 3 sin x - 4 cos x$
Replacing $- x$ by $x$ , we get
$\Rightarrow f (x) = - 3 sin (- x) - 4 cos (- x)$
$\Rightarrow f (x) = 3 sin (x) - 4 cos (x)$

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Similar questions

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Let f be an odd function defined on the real numbers such that f(x)=3sinx+4cosx, for x≥0, then f(x) for x<0 is

The correct option is A 3sinx−4cosxf(−x)=−f(x) for odd function ⇒f(−x)=−(3sinx+4cosx)⇒f(−x)=−3sinx−4cosx Replacing −x by x, we get ⇒f(x)=−3sin(−x)−4cos(−x) ⇒f(x)=3sin(x)−4cos(x)

Let $f$ be an odd function defined on the real numbers such that $f (x) = 3 sin x + 4 cos x$ , for $x \geq 0$ , then $f (x)$ for $x < 0$ is

The correct option is A $3 sin x - 4 cos x$
$f (- x) = - f (x)$ for odd function
$\Rightarrow f (- x) = - (3 sin x + 4 cos x) \Rightarrow f (- x) = - 3 sin x - 4 cos x$
Replacing $- x$ by $x$ , we get
$\Rightarrow f (x) = - 3 sin (- x) - 4 cos (- x)$
$\Rightarrow f (x) = 3 sin (x) - 4 cos (x)$