Gx-y-gx-gy-3xyx-y - x- y- R and g-0-4-For which of the following values of x is -gx not defined-

The correct option is D none of these g'(x) = lim_h→ 0g(x+h) g(x)/h=lim_h→ 0g(x)+g(h)+3hx(x+h) g(x)/h ⇒ g'(x) = lim_h→ 0g(h)+3hx(x+h)/h = 3x^2+g'(0) = ...

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Byju's Answer

Standard XII

Mathematics

Sum of Infinite Terms of a GP

gx+y=gx+gy+3x...

Question

$g (x + y) = g (x) + g (y) + 3 x y (x + y) \forall x, y ϵ R$ and $g^{'} (0) = - 4$ .For which of the following values of $x$ is $\sqrt{g (x)}$ not defined?

[- 2, 0]

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none of these

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Solution

The correct option is D none of these
$g^{'} (x) = lim h \to 0 \frac{g (x + h) - g (x)}{h} = lim h \to 0 \frac{g (x) + g (h) + 3 h x (x + h) - g (x)}{h}$
$\Rightarrow g^{'} (x) = lim h \to 0 \frac{g (h) + 3 h x (x + h)}{h} = 3 x^{2} + g^{'} (0) = 3 x^{2} - 4$
Now $\sqrt{g (x)}$ will not defined when $g^{'} (x) < 0$
$\Rightarrow 3 x^{2} - 4 < 0 \Rightarrow x \in (- \frac{2}{\sqrt{3}}, \frac{2}{\sqrt{3}})$

Suggest Corrections

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g(x+y)=g(x)+g(y)+3xy(x+y)∀x,yϵR and g′(0)=−4.For which of the following values of x is √g(x) not defined?

The correct option is D none of theseg′(x)=limh→0g(x+h)−g(x)h=limh→0g(x)+g(h)+3hx(x+h)−g(x)h⇒g′(x)=limh→0g(h)+3hx(x+h)h=3x2+g′(0)=3x2−4Now √g(x) will not defined when g′(x)<0⇒3x2−4<0⇒x∈(−2√3,2√3)

$g (x + y) = g (x) + g (y) + 3 x y (x + y) \forall x, y ϵ R$ and $g^{'} (0) = - 4$ .For which of the following values of $x$ is $\sqrt{g (x)}$ not defined?