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3 years ago

Evaluate the indicated function for f(x)=x^2-7 and g(x) =x-2

Mathematics

1 answer:

enyata [817]3 years ago

7 0

Answer:

f(g(x))=(x-2)^2 - 7

(x-2)(x-2) - 7

x^2-2x-2x+4-7

x^2-4x-3

g(f(x))=x^2-2-7

x^2-9

(x+3)(x-3)

Step-by-step explanation:

to solve for f(x), replace x with the g(x).
since we don't multiply a bracket with the negative or the positive signs to the
exponent, you have to factor into two binomials.
use the FOIL method to eliminate the brackets.
add like-terms

to find g(x), replace x with the f(x).
add like-terms
since there's difference of square, factor them into two binomials

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Consider the following equation. 9x2 − y2 = 6 (a) Find y' by implicit differentiation. y' = (b) Solve the equation explicitly fo

qaws [65]

Answer:

Step-by-step explanation:

Given is an equation in x and y as

$9x^2 - y^2 = 6$

We use implicit method to differentiate the above equation

18x-2yy'=0

y' = 9x/y

b) to solve the equation explicitly for y and differentiate to get y' in terms of x. y' = ±

We separate the variables as

$yy' =9x\\\frac{y^2}{2} =\frac{9x^2}{2} +C\\y^2 =9x^2+2C$

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2 years ago

Can someone help me with this. I tried to total all them up with 180 but none of the answers i got match the ones from the riddl

Vladimir79 [104]

Answer:

9. x=102

10. x=56

11. x=104

12. x=138

Step-by-step explanation:

9. In this problem, they are alternate exterior angles, meaning they are the same value. x=102

10. x is a corresponding angle, meaning they are the same. x=56

11. There are consecutive interior angles. The sum of these two angles is 180. to find x, subtract 76 from 180. 180-76 = 104 x = 104

12. These two angles are verticle angles, meaning they are equivalent. x = 138

6 0

2 years ago

Let f(x) = 1/x . Find the number b such that the average rate of change of f on the interval [2, b] is − 1/8

vekshin1

Answer:

b=4

Step-by-step explanation:

So, we have the function $f(x)=1/x$ . We need to find b such that the average rate of change or the slope is -1/8 between the intervel [2, b]. First, let's find f(2).

f(2) = 1/(2) = 1/2

So, we have the point (2, 1/2)

At point b, f(b) = 1/b.

Let's plug this into the slope formula:

$\frac{y_2-y_1}{x_2-x_1}=\frac{.5-\frac{1}{b} }{2-b} =-1/8$

Now, we just need to solve for b. First, let's multiply both the numerator and denominator by b (to get rid of the annoying fraction in the numerator).

$\frac{.5b-1}{2b-b^2} =\frac{-1}{8}$

Now, cross multiply.

$4b-8=b^2-2b$

$b^2-6b+8=0$

Solve for b. Factor using the numbers -4 and -2.

$=(b-4)(b-2)=0$

Thus, b=4 or b=2.

However, b=2 is not a possible solution since the interval [2,2] means nothing. Thus, b=4.

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2 years ago

(08.01, 8.02 MC) An expression is shown below: 18x3y − 9x2y − 72xy3 + 36y3 Part A: Rewrite the expression so the GCF is factored

vitfil [10]

Answer:

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Step-by-step explanation:

Given

18x³y - 9x²y - 72xy³ + 36y³ ← factor out 9y from each term

= 9y(2x³ - x² - 8xy² + 4y²)

Factor the first/second and third/fourth term in the parenthesis

= 9y( x²(2x - 1) - 4y²(2x - 1)) ← factor out (2x - 1) from each term

= 9y(2x - 1)(x² - 4y²)

x² - 4y² is a difference of squares and factors in general as

a² - b² = (a - b)(a + b), thus

x² - 4y²

= x² - (2y)² = (x - 2y)(x + 2y), hence

18x³y - 9x²y + 72xy³ + 36y³

= 9y(2x - 1)(x - 2y)(x + 2y) ← in factored form

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Step-by-step explanation:

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