The domain of the function f(x) = exp (sqrt { | vedclass

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(D) For the function $f(x) = \exp (\sqrt {5x - 3 - 2{x^2}} )$ to be defined,the expression under the square root must be non-negative.Thus,$5x - 3 - 2

Vedclass · Accepted Answer

$[1, 3/2]$

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(D) For the function $f(x) = \exp (\sqrt {5x - 3 - 2{x^2}} )$ to be defined,the expression under the square root must be non-negative.Thus,$5x - 3 - 2{x^2} \ge 0$.Multiplying by $-1$,we get $2{x^2} - 5x + 3 \le 0$.Factoring the quadratic expression: $2{x^2} - 2x - 3x + 3 \le 0 \implies 2x(x - 1) - 3(x - 1) \le 0 \implies (2x - 3)(x - 1) \le 0$.This can be written as $2(x - 3/2)(x - 1) \le 0$.Using the wavy curve method (sign scheme),the expression is $\le 0$ for $x \in [1, 3/2]$.Therefore,the domain is $[1, 3/2]$.

The domain of the function $f(x) = \exp (\sqrt {5x - 3 - 2{x^2}} )$ is

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