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valkas [14]
2 years ago
14

Find f(g(x)) and g(f(x)). f(x)=x²-2 and g(x)=√x+1

Mathematics
1 answer:
Archy [21]2 years ago
6 0

Answer:

1. x - 1

2. \sqrt{x^2-1}

Step-by-step explanation:

f(g(x)) = \sqrt{x+1}^2 - 2\\ = x + 1 - 2\\= x - 1

g(f(x)) =\sqrt{x^2-2+1}\\ = \sqrt{x^2-1}

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According to synthetic division below, which of the following statements are true ?
Whitepunk [10]

ANSWER

C

E

F

EXPLANATION

The result of the synthetic division is :

3 -1 0

The last number is the remainder which is 0

The first two numbers are the coefficients of the quotient.

Therefore the quotient is 3x -1

Since the remainder is 0, x-4 is a factor of

f(x) = 3 {x}^{2}  - 13x +  4

This also means that:

(3 {x}^{2}  - 13x +  4)  \div (x - 4) = 3x - 1

This again means that x=4 is a root of

f(x) = 3 {x}^{2}  - 13x +  4

The correct choices are C,E and F.

4 0
4 years ago
The polynomial p ( x ) = x 3 − 7 x − 6 p(x)=x 3 −7x−6p, left parenthesis, x, right parenthesis, equals, x, cubed, minus, 7, x, m
avanturin [10]

Answer:

p(x)=x^3-7x-6 = (x+1)(x+2)(x-3)

Step-by-step explanation:

Given that polynomial:

p(x)=x^3-7x-6

Known factor: (x+1)

To find:

Equation of the polynomial as the product of linear factors.

Solution:

The degree of polynomial is 3, and when we divide it by a linear equation, the result will be a quadratic.  That quadratic will have 2 solutions.

We can solve the quadratic in two linear factors and as a result we will have the answer.

First of all, we need to divide the polynomial p(x) with the given factor (x+1) to find the other factors.

\dfrac{x^3-7x-6}{x+1} = x^2-x-6

Solving the quadratic:

x^2-x-6 = x^2-3x+2x-6\\\Rightarrow x(x-3)+2(x-3)\\\Rightarrow (x+2)(x-3)

So, the answer is:

p(x)=x^3-7x-6 = (x+1)(x+2)(x-3)

4 0
3 years ago
Read 2 more answers
F(x) = x3 + 6x2 – x<br><br><br> f(x) = 30?
xxMikexx [17]

Answer and Step-by-step explanation:

The answer is 2 (which is equal to x).

If you were to plug 2 in to the function, the result if 30.

x^{3}+ 6x^{2} -x\\\\\\\\(2)^3+6(2)^2 - 2 = 30 = f(2)

<em><u>#teamtrees #PAW (Plant And Water)</u></em>

7 0
3 years ago
Please help me and I’ll give you brainiest!!!!!!!!!
Anon25 [30]
Y33x is your answer and
7 0
3 years ago
If y varies directly with x and y = -15 when x = 3, find x when y = 10.
Anika [276]

Answer:

like here x= 3 and y= -15

here, its 5 times goes in negative

now if y = 10 TO X IS 5 TIME POSITIVE HERE = 10×5 = 50

4 0
3 years ago
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