Q. 1045.0( 1 Vote )

State True or False for the statements

The composition of two continuous functions is a continuous function.

Answer :

True

Let f be a function defined by f(x) = |1-x + |x|| .


Let g(x) = 1-x + |x| and h(x) = |x| be two functions defined on R.


Then,


hog(x) = h(g(x))


hog(x) = h(1-x + |x|)


hog(x) = |(1-x + |x|)|


hog(x) = f(x) x R.


Since (1-x) is a polynomial function and |X| is modulus function are continuous in R.


g(x) = 1-x + |x| is everywhere continuous.


h(x) = |x| is everywhere continuous.


Hence, f = hog is everywhere continuous.


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