F - R - R is a function- If a - b - c -7- then which of the following is CORRECT- where- a-fx-fy-fzb - f x f y - f y f z - f z f x c-fx - fy - fzcorrect answer -2- wrong answer -0-50 A- a -3B- b -2C- a - b - c -3D- c -2

The correct option is D c = 2a+b+c=7 ∑ f(x)+∑ f(x)· f(y)+f(x)· f(y)· f(z)=7 Assuming t =f(x) and putting y =z =x, we get t^3+3t^2+3t 7 = 0 By observation, t=1, ...

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Byju's Answer

Standard XII

Mathematics

Geometrical Representation of a Complex Number

f : R → R is ...

Question

$f : R \to R$ is a function. If $a + b + c = 7,$ then which of the following is CORRECT?
where,
$a = f (x) + f (y) + f (z)$
$b = f (x) f (y) + f (y) f (z) + f (z) f (x)$
$c = f (x) \cdot f (y) \cdot f (z)$
(correct answer + 2, wrong answer - 0.50)

a = 3

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b = 2

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c = 2

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a - b + c = 3

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Solution

The correct option is C $c = 2$
$a + b + c = 7$
$\sum f (x) + \sum f (x) \cdot f (y) + f (x) \cdot f (y) \cdot f (z) = 7$
Assuming $t = f (x)$ and putting $y = z = x$ , we get
$t^{3} + 3 t^{2} + 3 t - 7 = 0$
By observation, $t = 1$ , so
$\Rightarrow (t - 1) (t^{2} + 4 t + 7) = 0$
Now,
$t^{2} + 4 t + 7 = 0 D = 16 - 28 < 0$
No real roots.
Therefore,
$f (x) = 1 = f (y) = f (z)$
Hence, $a = 3, b = 3, c = 1$

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f:R→R is a function. If a+b+c=7, then which of the following is CORRECT? where, a=f(x)+f(y)+f(z) b=f(x)f(y)+f(y)f(z)+f(z)f(x) c=f(x)⋅f(y)⋅f(z) (correct answer + 2, wrong answer - 0.50)

The correct option is C c=2a+b+c=7 ∑f(x)+∑f(x)⋅f(y)+f(x)⋅f(y)⋅f(z)=7 Assuming t=f(x) and putting y=z=x, we get t3+3t2+3t−7=0 By observation, t=1, so ⇒(t−1)(t2+4t+7)=0 Now, t2+4t+7=0D=16−28<0 No real roots. Therefore, f(x)=1=f(y)=f(z) Hence, a=3,b=3,c=1

$f : R \to R$ is a function. If $a + b + c = 7,$ then which of the following is CORRECT?
where,
$a = f (x) + f (y) + f (z)$
$b = f (x) f (y) + f (y) f (z) + f (z) f (x)$
$c = f (x) \cdot f (y) \cdot f (z)$
(correct answer + 2, wrong answer - 0.50)