Determine the range of f(x) = 2 extcos x + 1 and the period of g(x) = extsin 2x.

April 13, 2026Mathematics

ScanSolve AI Answer

April 13, 2026

Answer

[-1, 3]

Step 1: Determine the range of $f(x)$ . The function is $f(x) = 2\cos x + 1$ . The range of the cosine function is $-1 \le \cos x \le 1$ . Multiply by 2: $-2 \le 2\cos x \le 2$ . Add 1: $-2+1 \le 2\cos x + 1 \le 2+1$ . So, $-1 \le f(x) \le 3$ .

The range of $f$ is $\boxed{[-1, 3]}$ .

Step 2: Determine the period of $g(x)$ . The function is $g(x) = \sin 2x$ . For a function of the form $y = \sin(bx)$ , the period is $\frac{360^\circ}{|b|}$ . Here, $b=2$ . $Period = \frac{360^\circ}{2} = 180^\circ$

The period of $g$ is $\boxed{180^\circ}$ .

Step 3: Determine the values of $x$ for which

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Determine the range of f(x). The function is f(x) = 2 x + 1.

Asked on April 13, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on April 13, 2026

Step 1: Determine the range of f(x). The function is f(x) = 2 x + 1. The range of the cosine function is -1 x 1. Multiply by 2: -2 2 x 2. Add 1: -2+1 2 x + 1 2+1. So, -1 f(x) 3. The range of f is [-1, 3]. Step 2: Determine the period of g(x). The function is g(x) = 2x. For a function of the form y = (bx), the period is (360^)/(|b|). Here, b=2. Period = (360^)/(2) = 180^ The period of g is 180^. Step 3: Determine the values of x for which