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QuestionTentukan (f∘g)(5)(f \circ g)(5) untuk f(x)=x+2f(x)=x+2 dan g(x)=2x−1x+4,x≠−4g(x)=\frac{2 x-1}{x+4}, x \neq-4.

Studdy Solution

STEP 1

Assumptions1. We have two functions f(x)=x+f(x)=x+ and g(x)=x−1x+4g(x)=\frac{ x-1}{x+4}, with x≠−4x \neq-4. . We need to find the value of (f∘g)(5)(f \circ g)(5).

STEP 2

First, we need to understand what (f∘g)(x)(f \circ g)(x) means. It is the composition of functions ff and gg, which means we apply function gg first and then function ff.
(f∘g)(x)=f(g(x)) (f \circ g)(x) = f(g(x))

STEP 3

Now, we need to find the value of g(5)g(5).
g(5)=2⋅5−15+ g(5) = \frac{2 \cdot5 -1}{5 +}

STEP 4

Calculate the value of g()g().
g()=2⋅−1+4=99=1 g() = \frac{2 \cdot -1}{ +4} = \frac{9}{9} =1

STEP 5

Now that we have the value of g(5)g(5), we can find the value of (f∘g)(5)(f \circ g)(5), which is f(g(5))f(g(5)).
(f∘g)(5)=f(g(5))=f(1) (f \circ g)(5) = f(g(5)) = f(1)

STEP 6

Now, we need to find the value of f(1)f(1).
f(1)=1+2 f(1) =1 +2

STEP 7

Calculate the value of f(1)f(1).
f(1)=1+2=3 f(1) =1 +2 =3 So, the value of (f∘g)(5)(f \circ g)(5) is3.

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