Question

sendA função fogo é dada por F [g(x)]=11x+8e f(x)=2x+6 determine


g (x)




fog (-1)​

Answer 1

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⠀⠀☞ A função g(x) = (11x/2) + 1 e fog(-1) = -3. ✅

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$\Large\red{\sf a)\underline{\quad\qquad\qquad\qquad\qquad\qquad\quad}}$✍

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➡️⠀Seja g(x) = y. Desta forma temos que:

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$\LARGE\blue{\sf f(g(x)) = f(y) = 2 \cdot y + 6}$

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➡️⠀Temos, do enunciado, que f(g(x)) = 11 · x + 8. Portanto:

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$\blue{\Large\sf~f(g(x))~\begin{cases}\sf~I)~~ = 11 \cdot x + 8\\\\ \sf~II)~~ = 2 \cdot y + 6 \end{cases}}$

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➡️⠀Desta forma temos que I)  = II), ou seja:

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$\LARGE\blue{\sf 11 \cdot x + 8 = 2 \cdot y + 6}$

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➡️⠀Vamos portanto isolar y:

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$\LARGE\blue{\sf 2 \cdot y = 11 \cdot x + 8 - 6}$

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$\LARGE\blue{\sf 2 \cdot y = 11 \cdot x + 2}$

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$\LARGE\blue{\sf y = \dfrac{11 \cdot x + 2}{2}}$

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$\LARGE\blue{\sf y = \dfrac{11 \cdot x}{2} + 1}$  

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$\Large\green{\boxed{\rm~~~\red{a)}~\gray{g(x)}~\pink{=}~\blue{ \dfrac{11 \cdot x}{2} + 1 }~~~}}$ ✅

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$\Large\red{\sf b)\underline{\quad\qquad\qquad\qquad\qquad\qquad\quad}}$✍

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$\LARGE\blue{\sf f \circ g (-1) = 11 \cdot (-1) + 8}$

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$\LARGE\blue{\sf f \circ g (-1) = -11 + 8}$

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$\LARGE\blue{\sf f \circ g (-1) = -3}$

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$\Large\green{\boxed{\rm~~~\red{b)}~\gray{f \circ g (-1)}~\pink{=}~\blue{ -3}~~~}}$ ✅

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$\bf\large\red{\underline{\quad\quad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}$☁

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