Q find the domain of definition of f(x)=root(x-3-2root(x-4) ) - root (x-3+2root(x-4) ) Q find the domain of the - Maths - Relations and Functions

Question

Q find the domain of definition of f(x)=root(x-3-2root(x-4) ) -
root (x-3+2root(x-4) )
Q find the domain of the function f(x)=root(5mod(x) -x^2-6)
Q find the range of the function f(x)=x+2/mod(x+2),where x isnot
equal to -2

Vinay Kumar Sharma · Accepted Answer

find the domain of the function f(x)=root(5mod(x) -x^2-6) on squaring,

$f^{2} (x) = 5 | x | - x^{2} - 6 o n s o l v i n g, f^{2} (x) = x^{2} - 3 x - 2 x + 6 f^{2} (x) = (x - 2) (x - 3) \Rightarrow f (x) = \sqrt{(x - 2) (x - 3)} f (x) c a n n o t b e i m a g i m a r y, s o x c a n n o t b e 2 a n d 3 s o, t h e d o m a i n o f f (x) = {x \in R | x \geq 3}$ 3. Rnage of $f (x) = \frac{x + 2}{| x + 2 |}, x \neq - 2$

Range of a function can not be undefined so can not be -2.

so, for x=-1,

$f (x) = \frac{(- 1 + 2)}{| - 1 + 2 |} = 1 a n d f o r x = 1, f (x) = \frac{(1 + 2)}{| 1 + 2 |} = 1 h e n c e f o r e a c h v a l u e o f x f (x) g i v e s 1$ so the range of the function, f(x)= {R}

Q.find the domain of definition of f(x)=root(x-3-2root(x-4) ) - root (x-3+2root(x-4) ). Q.find the domain of the function f(x)=root(5mod(x) -x^2-6). Q.find the range of the function f(x)=x+2/mod(x+2),where x isnot equal to -2.

Q.find the domain of definition of f(x)=root(x-3-2root(x-4) ) - root (x-3+2root(x-4) ).

Q.find the domain of the function f(x)=root(5mod(x) -x^2-6).

Q.find the range of the function f(x)=x+2/mod(x+2),where x isnot equal to -2.