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Elena L [17]
2 years ago
12

If f left parenthesis x right parenthesis equals short dash 4 x minus 8 and g left parenthesis x right parenthesis equals 3 x sq

uared plus x, then f left parenthesis short dash 1 right parenthesis g left parenthesis 2 right parenthesis =
Mathematics
1 answer:
Len [333]2 years ago
8 0

The answer is -56

f(x)=-4x-8\\\\g(x)=3x^{2}+x

f(-1) = -4(-1)-8= 4-8 =-4

g(2) = 3(2)^2+2 = 12+2 = 14

therefore the multiplication of functions, f(-1)g(2) = (-4)*(14) =-56

The answer is -56

learn more about multiplication of functions here:

brainly.com/question/18042673

#SPJ1

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zzz [600]

Answer:

\theta  = \frac{\pi}{3} ,  \pi, \frac{5\pi}{ 3}

Step-by-step explanation:

we want to solve the following trigonometric equation:

\displaystyle  - 2 { \sin}^{2}  (\theta )+  \cos( \theta)  + 1 = 0,  \:  \theta \in [0,2\pi)

The first step of solving trigonometric equation is to rewrite the equation in terms of one trigonometric function . With Pythagorean theorem, we know that sin²x=1-cos²x . It will be helpful to rewrite the equation in terms of one trig functions. Therefore, substitute 1-cos²\theta in the place of sin²\theta:

\displaystyle  - 2 (1 -  \cos  ^{2} ) +  \cos( \theta)  + 1 = 0,  \:  \theta \in [0,2\pi)

simplify:

\displaystyle\implies  - 2 (1 -  \cos  ^{2} (\theta) +  \cos( \theta)  + 1 = 0,  \:  \theta \in [0,2\pi)\\\implies- 2  +  \cos  ^{2} (\theta)+  \cos( \theta)  + 1 = 0,  \:  \theta \in [0,2\pi)\\\implies\cos  ^{2} (\theta)+  \cos( \theta)  -1 = 0

Consider cos² \theta\implies x. Thus,

2 {x}^{2}  + x  - 1 = 0

solving the quadratic equation yields:

{x}^{}   =  \frac{1}{2}    \\  x  =  - 1

back-substitute:

\begin{cases}  \cos( \theta)     =  \dfrac{1}{2}    \\    \cos( \theta)   =  - 1  \end{cases}  \theta \in[0,2\pi)

take inverse trig in both sides

\implies \begin{cases}   \theta  =   \dfrac{\pi}{3}   + 2n\pi\\\theta= \frac{5\pi}{3}   +  2n\pi   \\    \theta   =  \pi + 2n\pi\end{cases}  \theta \in[0,2\pi)  \\\\\implies\theta= \frac{\pi}{3}+\dfrac{2n\pi}{3},\theta\in [0,2\pi)\\\text{when n=0}\\ \implies   \theta  = \frac{\pi}{3} \\ \text{when n=1}\\ \theta= \pi\\ \text{when n=2}\\\theta=\frac{5\pi}{ 3}

In conclusion,

\displaystyle\theta  = \frac{\pi}{3} ,  \pi, \frac{5\pi}{ 3}

7 0
2 years ago
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