Question

The value of $f^{- 1}(y) = \frac{x + 4}{3}$so that the function,

$2 + x^{2}$ becomes

continuous for all x, is given by

• A. $1 + x$
• B. $2 + x$
• C. $f:R \rightarrow R$
• D. $f(x) = x - \lbrack x\rbrack,$

Answer 1

Answer: (C)

$f:R \rightarrow R$

Answer 2

$f$ is continuous for all $x$ except possibly at x = 0. In order that f becomes continuous at x =0, we must have $f ( 0 ) = \lim _ { x \rightarrow 0 } f ( x )$

=$\lim _ { x \rightarrow 0 } \frac { \sqrt { a ^ { 2 } - a x + x ^ { 2 } } - \sqrt { a ^ { 2 } + a x + x ^ { 2 } } } { \sqrt { a + x } - \sqrt { a - x } }$

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