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Gemiola [76]
3 years ago
13

F(x)=2x+1 and g(x)=x^2-7, find (f g) (x)

Mathematics
1 answer:
hodyreva [135]3 years ago
5 0

The answer is (f o g)(x) = 2x^2 - 13

In order to find a composite function, you take the first letter (in this case f) and use that equation. You then remove the variable and put in the second letter (g).

f(x) = 2x + 1 ----> Remove variable.

f(x) = 2(      ) + 1 ----> Insert g(x)

(f o g)(x) = 2(x^2 - 7) + 1 ----> Distribute

(f o g)(x) = 2x^2 - 14 + 1 ----> Simplify

(f o g)(x) = 2x^2 - 13

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Use the order of operations to evaluate this expression: 7 + (5 – 9)2 + 3(16 ÷ 8).
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Remember to use PEMDAS when solving.

=  7 + (5 – 9)2 + 3(16 ÷ 8)

= 7 + (-4)2 + 3(2)

= 7 + (-8) + 6

= -1 + 6

= 5

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I'll assume that each cabbage weighs p pounds.

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The time a projectile spends in the air can be modeled by the equation t² -t - 8 = 0, in which t represents the amount of time t
s2008m [1.1K]

Answer:

(t - 4)(t + 2) = 0  

Step-by-step explanation:

The general formula for a quadratic expression is

y = ax² + bx + c

Your expression is

y = t² - 2t - 8 = 0

By comparison, we see that

a = 1; b = -2; c = -8

1. Find two numbers that multiply to give ac and add to give b.

In this case, find two numbers that multiply to give -8 and add to give -2.

It helps to list the factors of  -8.

They are ±1, ±2, ±4, and ±8

After a little trial and error, you should find the numbers -4 and +2.

-4 × 2 = -8, and -4 + 2 = -2)

2. Rewrite the middle term with those numbers

t² -4t + 2t - 8 = 0

3. Factor the first and last pairs of terms separately

t(t - 4) +2(t - 4) = 0

4. Separate the common factor

The common factor is t - 4.

(t - 4)(t + 2) = 0

8 0
3 years ago
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