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olga55 [171]
3 years ago
13

F(x) = x − 8, g(x) = |x + 8| Find (f ∘ g)(x).

Mathematics
1 answer:
miskamm [114]3 years ago
5 0

Answer:

<h2>(f  \circ g)(x) =  |x  +  8|  - 8</h2>

Step-by-step explanation:

f(x) = x - 8 \\  \\ g(x) =  |x + 8|

To find (f ∘ g)(x) , substitute g(x) into f(x). That is for every x in f (x) replace it with g (x)

That's

<h3>(f  \circ g)(x) =  |x  +  8|  - 8</h3>

Hope this helps you

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The relationship between x and y is represent as:

Since, the relationship is linear.

The standard form of equation of line is:

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\text{Substitute x}_1=-2,y_1=10,x_2=-1,y_2=7.5\text{ in the standard equation of line.}

\begin{gathered} y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \\ y-10=\frac{7.5-10}{-1-(-2)}(x-(-2)) \\ y-10=\frac{-2.5}{1}(x+2) \\ y-10=-2.5(x+2) \\ y=-2.5(x+2)+10 \end{gathered}

The equation of the linear relationship between x and y is:

y = -2.5(x + 2) + 10

Now, to check that the point (9, -17.5) lies on the represented relationship between x and y

Substitute x = 9 and y = -17.5 in the equation y = -2.5(x + 2) + 10

y = -2.5(x + 2) + 10

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Thus, LHS = RHS

Hence the point (9, -17.5) lie on the given linear relationship between x and y.

Answer: The point (9, -17.5) lie on the given linear relationship between x and y.

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