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# Range

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The range of the function g(x) = 2/(2 + 4x + 3x^2) can be written as an interval (a,b]. What is a+b?

Jun 22, 2022

#1
+13793
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What is a+b?

Hello Guest!

$$g(x)=2/f(x)\\ f(x)=3x^2+4x+2\\ \frac{df(x)}{dx}=6x+4=0\\ x_{max}=-\dfrac{2}{3}\\ {\color{blue}g(x)_{max}=}2/(3\cdot \frac{4}{9}-\frac{8}{3}+2)=\color{blue}3$$

$$R\in \mathbb R$$  |  0 < R $$\leq$$ 3

$$\color{blue}a + b = 0 + 3 = 3$$

!

Jun 22, 2022
edited by asinus  Jun 22, 2022
edited by asinus  Jun 22, 2022