If f and g are two functions defined as fx - x - 2- x - 0- g x - 3- x - 0-then the domain of f - g is

To find out about the domain off + g:f(x) = x + 2,0ex0exx ≤ 0 0ex0exg(x) ...

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Standard XII

Mathematics

Greatest Integer Function

If f and g ar...

Question

If f and g are two functions defined as $f (x) = x + 2, x \leq 0; g (x) = 3, x \geq 0,$ then the domain of $f + g$ is

${0}$

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$[0, \infty)$

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$(- \infty, \infty)$

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$(- \infty, 0)$

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Solution

The correct option is A
${0}$

To find out about the domain of $f + g$ :
$f (x) = x + 2, x \leq 0 g (x) = 3, x \geq 0$
Domain of $f (x) = (- \infty, 0]$
Domain of $g (x) = [0, \infty)$
Domain of $(f + g) = (- \infty, 0] \cap [0, \infty)$
$= {0}$
Hence, option A is the correct is the answer.

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Similar questions

If f, g, h are real functions defined by $f (x) = \sqrt{x + 1}, g (x) = \frac{1}{x}$ and $h (x) = 2 x^{2} - 3$ , then find the values of (2f + g - h) (1) and (2f + g - h) (0).

Q. If f, g and h are real functions defined by

f (x) = \sqrt{x + 1}, g (x) = \frac{1}{x}

and h(x) = 2x² − 3, find the values of (2f + g − h) (1) and (2f + g − h) (0).

Q. Assertion(A):

f (x) = log (x - 2) + log (x - 3)

and

g (x) = log (x - 2) (x - 3)

then

f (x) = g (x)

Reason (R): Two functions

f (x)

and

g (x)

are said to be equal if they are defined on the same domain

A

and the co-domain

B

f (x) = g (x) \forall x \in A

If f(x) , g(x) and h(x) are three differentiable functions throughout their domains and given that their first derivatives are -

$f^{'} (x) < 0$

$g^{'} (x) = 0$

$h^{'} (x) \leq 0$

throughout their domains. Then choose the correct option of monotonically decreasing functions -

Q. A function f is defined on [-1,1] as
f(x)={-x+1/2 ; -1≤x {x+1/2. ; 0≤x≤1
And if g(x) = |f(x)|+f(|x|) then find
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If f and g are two functions defined as f(x)=x+2,x≤0;g(x)=3,x≥0,then the domain of f+g is

The correct option is A {0}To find out about the domain off+g:f(x)=x+2,x≤0g(x)=3,x≥0Domain of f(x)=(-∞,0]Domain of g(x)=[0,∞)Domain of (f+g)=(-∞,0]∩[0,∞)={0}Hence, option A is the correct is the answer.

If f and g are two functions defined as $f (x) = x + 2, x \leq 0; g (x) = 3, x \geq 0,$ then the domain of $f + g$ is

The correct option is A
${0}$

To find out about the domain of $f + g$ :
$f (x) = x + 2, x \leq 0 g (x) = 3, x \geq 0$
Domain of $f (x) = (- \infty, 0]$
Domain of $g (x) = [0, \infty)$
Domain of $(f + g) = (- \infty, 0] \cap [0, \infty)$
$= {0}$
Hence, option A is the correct is the answer.