Question

Discuss the continuity of the function f given by f(x) = x³ + x ² –1.

Solution

Here f(x) = x³ + x² –1
Function f is defined for all real numbers.
Let c be any real number
$therefore space straight f left parenthesis straight c right parenthesis equals straight c cubed plus straight c squared minus 1 Also space Lt with straight x rightwards arrow straight c below straight f left parenthesis straight x right parenthesis equals Lt with straight x rightwards arrow straight c below left parenthesis straight x cubed plus straight x squared minus 1 right parenthesis equals straight c cubed plus straight c squared minus 1 therefore space Lt with straight x leftwards arrow straight c below straight f left parenthesis straight x right parenthesis equals straight f left parenthesis straight c right parenthesis$
∴ f is continuous at c
But c is any real number
∴ f is continuous at every real number
∴ f is continuous function.

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Continuity And Differentiability

Discuss the continuity of the function f given by f(x) = x³ + x ² –1.

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Discuss the continuity of the function f given by f(x) = x³ + x ² –1.