Let fx-3-x-2-1-x-3 and gx-x2-4 x-19-x2-x-6- If fx-gx- then x-

The correct options are C 4f(x) = 3x 2 1x+3 Domain of f(x) is nbsp; x ∈ℝ { 3, 2} And g(x) = x^2 4x+19x^2+x 6 ⇒ g(x) = x^2 4x+19(x+3)(x 2) Domain of g(x) is ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XI

Mathematics

Domain

Let fx=3/x-2-...

Question

Let $f (x) = \frac{3}{x - 2} - \frac{1}{x + 3}$ and $g (x) = \frac{x^{2} - 4 x + 19}{x^{2} + x - 6}$ . If $f (x) = g (x)$ , then $x =$

2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

4

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

6

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $4$
$f (x) = \frac{3}{x - 2} - \frac{1}{x + 3}$
Domain of $f (x)$ is
$x \in R - {- 3, 2}$
And
$g (x) = \frac{x^{2} - 4 x + 19}{x^{2} + x - 6} \Rightarrow g (x) = \frac{x^{2} - 4 x + 19}{(x + 3) (x - 2)}$
Domain of $g (x)$ is
$x \in R - {- 3, 2}$

$f (x) = g (x) \Rightarrow \frac{3}{x - 2} - \frac{1}{x + 3} = \frac{x^{2} - 4 x + 19}{(x + 3) (x - 2)} \Rightarrow \frac{2 x + 11}{(x - 2) (x + 3)} = \frac{x^{2} - 4 x + 19}{(x - 2) (x + 3)} \Rightarrow 2 x + 11 = x^{2} - 4 x + 19 (∵ x \neq - 3, 2) \Rightarrow x^{2} - 6 x + 8 = 0 \Rightarrow (x - 2) (x - 4) = 0 \Rightarrow x = 4 (∵ x \neq 2)$

Suggest Corrections

Similar questions

Q. If

f (x) = \frac{x^{2} - 1}{x}

and

g (x) = \frac{x + 2}{x - 3},

then the domain of

\frac{f (x)}{g (x)}

Q. If

f (x) = \frac{2}{x - 3}

g (x) = \frac{x - 3}{x + 4}

and

h (x) = - \frac{2 (2 x + 1)}{x^{2} + x - 12}

, then

lim x \to 3 [f (x) + g (x) + h (x)]

Q. Assertion :Let the function

f (x) = x^{2} - x + 1 \forall x \geq \frac{1}{2}

and

g (x) = \frac{1}{2} + \sqrt{x - \frac{3}{4}}

, then

f (x) = g (x)

has two solutions. Reason:

f (x)

and

g (x)

are inverse of each other.

Q. Let f(x) =

x^{2} + \frac{1}{x^{2}}

and g(x) = x -

\frac{1}{x}, x \in R - {- 1, 0, 1} . I F h (x) = \frac{f (x)}{g (x)}, t h e n t h e l o c a l m i n i m u m v a l u e o f h (x) i s :

Q. If

f (x) = \frac{2}{x - 3}, g (x) = \frac{x - 3}{x + 4}

and

h (x) = \frac{- 2 (2 x + 1)}{x^{2} + x - 12}

, then

lim x \to 3 [f (x) + g (x) + h (x)]

is equal to:

Join BYJU'S Learning Program

Let f(x)=3x−2−1x+3 and g(x)=x2−4x+19x2+x−6. If f(x)=g(x), then x=

Let $f (x) = \frac{3}{x - 2} - \frac{1}{x + 3}$ and $g (x) = \frac{x^{2} - 4 x + 19}{x^{2} + x - 6}$ . If $f (x) = g (x)$ , then $x =$