The domain of the function f(x) = e^{sqrt{5x | vedclass

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Question

(C) For the function $f(x) = e^{\sqrt{5x - 3 - 2x^2}}$ to be defined, the expression under the square root must be non-negative:$5x - 3 - 2x^2 \ge 0$M

Vedclass · Accepted Answer

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

Vedclass · Answer

(C) For the function $f(x) = e^{\sqrt{5x - 3 - 2x^2}}$ to be defined, the expression under the square root must be non-negative:$5x - 3 - 2x^2 \ge 0$Multiply by $-1$ and reverse the inequality:$2x^2 - 5x + 3 \le 0$Factor the quadratic expression:$2x^2 - 2x - 3x + 3 \le 0$$2x(x - 1) - 3(x - 1) \le 0$$(2x - 3)(x - 1) \le 0$The roots are $x = 1$ and $x = \frac{3}{2}$.For the product to be $\le 0$, $x$ must lie between the roots inclusive:$1 \le x \le \frac{3}{2}$Thus, the domain is $[1, \frac{3}{2}]$.

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

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