Find g(2/3). Simplify your answer. Type an exact answer, using radicals as needed).

Mathematics

1 answer:

ki77a [65]3 years ago

5 0

The solution is 2sqrt77/77. You just fill in 2/3 for the x's. When you do that, you do that you get (2/3)/sqrt(9-[2/3]^2) which, simplified, is (2/3)/sqrt(9-[4/9]). Now use the common denominator under the radical of 9 to get (2/3)/sqrt([81-4]\9). Simplifying even further gives you (2/3)/([sqrt(77)]/3). Now do that division by multiplying 2/3 by the reciprocal of ([sqrt(77)]/3) to get 2/sqrt77. I rationalized the denominator to get that result up there.

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Answer

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Explanation

We are given that

f(x) = (2 - x)/(x + 1)

g(x) = 18 - 3x

We are then asked to find (f o g)(x)

(f o g) (x) is the same as writing the expression for f(x) but instead of x, we will write g(x) in the expression.

$\begin{gathered} f(x)=\frac{2-x}{x+1} \\ (\text{fog)(x) = }\frac{2-g(x)}{g(x)+1} \end{gathered}$

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So,

$\begin{gathered} (\text{fog)(x) = }\frac{2-g(x)}{g(x)+1} \\ (\text{f o g)(x) = }\frac{2-(18-3x)}{18-3x+1} \\ (f\text{ o g)(x) = }\frac{2-18+3x}{17-3x} \\ (f\text{ o g)(x) = }\frac{-16+3x}{17-3x} \\ (f\text{ o g)(x) = }\frac{3x-16}{17-3x} \end{gathered}$

Hope this Helps!!!

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