Trying to find the right answer to this..

Here f(x) = sin (x 2 ) Let g(x) =sinx and h(x) = x2 ∴(g o h) (x) = g (h(x)) = g(x 2 ) = sin x 2 Now f(x) = (g o h)(x) and g, h are both continuous functions. ∴ f is continuous function.

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Continuity and Differentiability

Short Answer Type

121.

Find the values of a and b such that the function defined by
$straight f left parenthesis straight x right parenthesis equals open curly brackets table row cell 5 comma end cell row cell ax plus straight b comma end cell row cell 21 comma end cell end table close table row cell if space straight x less or equal than 2 space space space space space space space space space space end cell row cell if space 2 less than straight x less than 10 end cell row cell if space straight x greater or equal than 10 space space space space space space space space end cell end table$
is a continous function.

116 Views

122. Show that the function defined by f(x) = sin (x² ) is a continuous function.

Here f(x) = sin (x²)
Let g(x) =sinx and h(x) = x2
∴(g o h) (x) = g (h(x)) = g(x² ) = sin x²Now f(x) = (g o h)(x) and g, h are both continuous functions.
∴ f is continuous function.

88 Views