I have some doubt in example -1 of lesson-2 in the chapter continuity and differentiability (maths xii)

to clear my doubt please check the question and solution first.

For what values of*x*is the functioncontinuous?

**Solution:**

Let*g*(*x*) = sin*x*,*h*(*x*) = |*x*|

Then, numerator of*f*(*x*) = |sin*x*| =*h*(*g*(*x*))

Since*g*and*h*are continuous functions, the numeration of*f*(*x*) is also continuous for all real*x*.

[Functional composition of 2 continuous functions is also continuous]

Now, consider the denominator of*f*(*x*), which is.

Let*g*(*x*) = 4,*h*(*x*) =*x* ^{2}− 9, and*k*(*x*) =

Functions*g*and*h*are continuous for all values of*x*since both are polynomials.

Function*k*is continuous for all*x*≥0

Now,*h*(*x*) =*x* ^{2}− 9 = (*x*+ 3) (*x*− 3)

⇒*h*(*x*) = 0, when*x*= 3 or*x*= −3

∴*h*(*x*)≥0 for*x*≥3 and*x*≤−3

⇒*k*(*h*(*x*)) =is continuous for*x*≥3 and*x*≤−3

Thus, the denominator of*f*(*x*) =is continuous for*x*≥3 and*x*≤−3

Thus, the denominator of*f*(*x*) =is continuous for*x*≥3 and*x*≤−3

However, for the function*f*to be defined, denominator should never be 0.

If= 0,

then*x* ^{2}− 9 = 16

⇒*x*=±5

Thus, denominator is zero, if*x*= 5 or*x*= −5

∴*f*(*x*) =is continuous for*x*≥3 and*x*≤3

when the question started to find the value of X for continuity of function while the answer was given for the functio*f* ( *x* ) = (sorry value of x is not included). i have joinned meritnation just 4-5 days before & found lots of errors . some clerical & some calculative. in this situation how i will be able to catch my mistakes & how will i study.

I have checked the said your query.

The statement of the question should be:

"For what values of *x *is the function *f* ( *x* ) = is continuous?

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