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

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Question

(A) 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:$5x - 3 - 2{x^2}

Vedclass · Accepted Answer

$\left[ {1, \frac{3}{2}} \right]$

Vedclass · Answer

(A) 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:$5x - 3 - 2{x^2} \ge 0$Multiply by $-1$ and reverse the inequality sign:$2{x^2} - 5x + 3 \le 0$Factor the quadratic expression:$2{x^2} - 2x - 3x + 3 \le 0$$2x(x - 1) - 3(x - 1) \le 0$$(2x - 3)(x - 1) \le 0$$2(x - 1)(x - 1.5) \le 0$Using the wavy curve method,the expression is $\le 0$ for $x \in [1, 1.5]$.Thus,the domain is $\left[ {1, \frac{3}{2}} \right]$.

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

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