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3 years ago

F(x) = x2+ x–1 and g(x) = x+ 3, what is f o g(x)

Mathematics

1 answer:

Naddika [18.5K]3 years ago

4 0

Answer:

Step-by-step explanation:

$f(x) = x^2 + x - 1\\g(x) = x +3\\\\\\(f\:o\:g)(x) = f(g(x))$

we input the function g(x) into every x in f(x)

$f(g(x)) = (x+3)^2 + (x + 3) - 1\\f(g(x)) = x^2 + 6x + 9 + x + 3 - 1\\f(g(x)) = x^2 + 7x + 11$

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Write in slope-intercept form an equation of the line that passes through the points (−1,12) and (1,2).

zzz [600]

Answer:

$y=-5x+7$

Step-by-step explanation:

step 1

Find the slope

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

the points (−1,12) and (1,2)

substitute

$m=\frac{2-12}{1+1}$

$m=\frac{-10}{2}$

$m=-5$

step 2

we know that

The equation of the line in slope intercept form is equl to

$y=mx+b$

where

m is the slope

b is the y-intercept

we have

$m=-5$

$point\ (1,2)$

substitute in the linear equation and solve for b

$2=-5(1)+b$

$b=2+5=7$

therefore

$y=-5x+7$

4 0

3 years ago

.<br> Put f(x) = x2 + 3 in y2.

saveliy_v [14]

Answer:

(X2+3)2

Step-by-step explanation:

First, you have to substitute in what f(x) equals for y since f(x) stands for y.

By doing this, the equation turns into (x2+3)2, because x2+3 is y, and 2 because the original equation way y2.

After you substitute, the answer is (x2+3)2.

5 0

2 years ago

How do I solve this? help please! xx

Anna35 [415]

This graph is composed of four straight line segments. You'll need to determine the slope, y-intercept and domain for each of them. Look at the first segment, the one on the extreme left. Verify yourself that the slope of this line segment is 1 and that the y-intercept would be 0 if you were to extend this segment all the way to the y-axis. Thus, the rule (formula, equation) for this line segment would be f(x)=1x+0, or just f(x)=x, for (-3,-1). Use a similar approach to write rules for the remaining three line segments.

Present your answer like this:
x, (-3,-1)
f(x) = -1, (-1,0)
one more here
one more here

5 0

3 years ago

Figure A

Amiraneli [1.4K]

<h2>Answer:</h2>

Figure B

<h2>Step-by-step explanation:</h2>

The Pythagorean Theorem is $a^2 + b^2 = c^2$ , where c is the longest side of the triangle (the hypotenuse).

To find the side length of each square, you have to square root the area of each square. This means that Figure A has side lengths of 3, 6 and 8 units. Figure B has side lengths of 5, 12 and 13 units.

In Figure A, if the triangle is right-angled, the equation $3^2 + 6^2 = 8^2$ must be correct. 9 + 36 = 45. 45 is not equal to 64, so the triangle is not right-angled.

In Figure B, if the triangle is right-angled, the equation $5^2 + 12 ^2 = 13^2$ must be correct. 25 + 144 = 169. 169 is 13 squared, so the triangle is right-angled.

Alternatively, as you are already given the square values for each side length, there is no need to square root and square again. You can just test if the two smaller areas equal the larger area, but the explanation above uses a more detailed example of the Pythagorean Theorem.

8 0

2 years ago

Read 2 more answers

Find soluton to x^2-14x+49=25

Artyom0805 [142]

$\boxed{x=12 \ and \ x=2}$

<h2>Explanation:</h2>

In this exercise, we have the following equation:

$x^2-14x+49=25$

We can write this Quadratic Equation in Standard Form as follows:

$x^2-14x+49=25 \\ \\ Subtract \ 25 \ from \ both \ sides: \\ \\ x^2-14x+49-25=25-25 \\ \\ x^2-14x+24=0 \\ \\$

So this is a Non-perfect Square Trinomial. To factor out this, let's choose two numbers such that:

The sum is -14
The product is 24

Those numbers are:

-12 and -2
SUM: -12-2 = -14
PRODUCT: (-12)(-2)=24

So we can write this as:

$x^2 + (a + b)x + ab=(x + a)(x + b) \\ \\ a=-12 \\ b=-2 \\ \\ x^2-14x+24=(x-12)(x-2)=0 \\ \\ So \ the \ solutions \ are: \\ \\ \boxed{x=12 \ and \ x=2}$

<h2>Learn more:</h2>

Quadratic Ffrmua: brainly.com/question/10188317

#LearnWithBrainly

6 0

3 years ago