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Troyanec [42]
3 years ago
14

F (x) = x^2 + 2x - 5 g(x) = 2x + 4 What is (f• g)(x)?

Mathematics
1 answer:
Vilka [71]3 years ago
5 0

Answer:

Step-by-step explanation:

This is a composite function, f(g(x)). This means, working from the inside function to the outside, we will take the function g and plug it in for x in the f function. g(x) = 2x + 4. We will plug that into f(x) and evaluate f(2x+4):

f(g(x))=(2x+4)^2+2(2x+4)-5 and I imagine your teacher has you simplify completely. We FOIL and distribute to get

f(g(x))=4x^2+16x+16+4x+8-5 which, by combining like terms, give us

f(g(x))=4x^2+20x+19

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Answer: \sum_{n=1}^{5}4^n=1364

Step-by-step explanation:

Since we have given that

\sum_{n=1}^{5}4^n

Now, we know the rule for summation , we'll apply this ,

\sum_{n=1}^{5}4^n\\=4^1+4^2+4^3+4^4+4^5\\

Now, it becomes geometric progression, so we us the formula for sum of terms in g.p. which is given by

S_n=\frac{a(r^n-1)}{r-1}\\\\\text{where 'a' is the first term and 'r' is the common ratio}

So, our equation becomes ,

a=4 \\\\r=\frac{a_2}{a_1}=\frac{4^2}{4}=4\\\\S_5=\frac{4(4^5-1)}{4-1}\\\\S_5=1364

Hence ,

\sum_{n=1}^{5}4^n=1364

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