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 ofxis the functioncontinuous?

Solution:

Letg(x) = sinx,h(x) = |x|

Then, numerator off(x) = |sinx| =h(g(x))

Sincegandhare continuous functions, the numeration off(x) is also continuous for all realx.

[Functional composition of 2 continuous functions is also continuous]

Now, consider the denominator off(x), which is.

Letg(x) = 4,h(x) =x 2− 9, andk(x) =

Functionsgandhare continuous for all values ofxsince both are polynomials.

Functionkis continuous for allx≥0

Now,h(x) =x 2− 9 = (x+ 3) (x− 3)

h(x) = 0, whenx= 3 orx= −3

h(x)≥0 forx≥3 andx≤−3

k(h(x)) =is continuous forx≥3 andx≤−3

Thus, the denominator off(x) =is continuous forx≥3 andx≤−3

Thus, the denominator off(x) =is continuous forx≥3 andx≤−3

However, for the functionfto be defined, denominator should never be 0.

If= 0,

thenx 2− 9 = 16

x=±5

Thus, denominator is zero, ifx= 5 orx= −5

f(x) =is continuous forx≥3 andx≤3

when the question started to find the value of X for continuity of function while the answer was given for the functiof ( 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?

We appreciate your bringing the errors to our notice. The said question will be corrected and updated very soon. We shall most definitely try and ensure that such errors do not occur in the future.

 

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