Question

To three decimal places, find the value of the first positive x-intercept for the function f(x) = 2cos(x + 3).

2.712
−1.429
1.712
−1.712

Answer 1

it is definitely not b 

Answer 2

Answer:

The first positive x-intercept for the function $f(x) = 2cos(x + 3)$ is $(1.712, 0)$.

Step-by-step explanation:

The x-intercept is the point where a line crosses the x-axis,

To find the x-intercept for the function $f(x) = 2cos(x + 3)$, let's substitute f(x) = 0 into the equation and solve for x:

$2\cos \left(x+3\right)=0\\\\\frac{2\cos \left(x+3\right)}{2}=\frac{0}{2}\\\\\mathrm{General\:solutions\:for}\:\cos \left(x+3\right)=0\\\\x+3=\frac{\pi }{2}+2\pi n,\:x+3=\frac{3\pi }{2}+2\pi n$

We want the value of the first positive x-intercept so we take the value of $x=\frac{3\pi }{2}+2\pi n-3$ when n = 0.

$x=\frac{3\pi}{2}+2\pi\cdot 0-3\\\\x=\frac{3\pi }{2}-3\approx 1.712$

We can check our answer with the graph of the function. We can see that we get the same answer.