If f(x) = 3x + 2 and g(x) = x^2 + 1, which expression is equivalent to (g(f(x))?

Answers

Answer 1

Answer: Whenever we are given one function and must calculate a funciton of the funciton, such as g(f(x)) in this case, we simply substitute the second function, f(x) in this case, in the first function, g(x) in this case, wherever the first function has a variable. Therefore,g(f(x)) = (3x + 2)^2 + 1g(f(x)) = 9x^2 + 12x + 4 + 1g(f(x)) = 9x^2 + 12x + 5

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which statement could be used to explain why f(x) = 2x – 3 has an inverse relation that is a function? a. the graph of f(x) passes the vertical line test. b. f(x) is a one-to-one function. c. the graph of the inverse of f(x) passes the horizontal line test. d. f(x) is not a function.

Answers

f(x) is a one-to-one function.

B- f(x) is a one-to-one function

What are all possible values of x that make a true statement?
95 – 2x < 7 (15x – 17)

Answers

Answer:

x = 2

Step-by-step explanation:

From the question we are given the algebraic sign with the Inequality sign

95 - 2x < 7 (15x - 17)

In order to find all the possible values of x that makes the algebraic expression true ,

We solve for this by convert the less than(<) sign to =

A true statement or algebraic expression is when both values on the left hand side and right hand side of and algebraic expression is the same of equal to each other.

Therefore:

95 - 2x = 7 (15x - 17)

95 - 2x = 105x - 119

Collect like terms

95 + 119 = 105x + 2x

214 = 107x

x = 214/107

x = 2

In other to confirm if x = 2 makes the expression true

95 - 2x = 7 (15x - 17)

95 - 2x = 105x - 119

95 - 2 × 2 = 105 × 2 - 119

95 - 4 = 210 - 119

91 = 91

Therefore, the possible values for x that make the statement true is x = 2

PLEASE HELP WILL GIVE BRAINIEST1.

Which is the equation of the given line in ponit-slope form?

A. y + 4 = 9/8(x + 1)

B. y + 1 = 8/9(x + 4)

C. y + 1 = 8/7(x + 4)

y - 1 = 8/9(x - 4)

(SAME IMAGE FOR QUESTION 2)

2.

Write the equation of the line in standard form.

A. -8x + 9y = 23

B. -8x + 9y = -23

C. -8x + 7y = 25

D. -9x + 8y = -23

Answers

Answer:

1. B

2. A $(y+1)=(8)/(9) (x+4)\ny+1=(8)/(9) x+(8)/(9) *4\ny+1=(8)/(9) x+(32)/(9)\n9*(y+1=(8)/(9) x+(32)/(9))\n9y+9=8x+32\n-8x+9y=32-9\n-8x+9y=23$

Step-by-step explanation:

The point slope form of a line is $(y-y_1)=m(x-x_1)$ where $x_1=-4\ny_1=-1$ . We write

$(y--1)=m(x--4)\n(y+1)=m(x+4)$

To find m, count the slope from each marked point on the graph. Notice one is 1/2 so we will count by halves. The slope is 8/9

This means B is the point slope form. To convert to the standard form, it must be written as $ax^2+by^2=c$ . We convert using inverse operations.

The quadratic equation (3k-2)x^2 +12x+3(k+1) =0 has equal roots. Find the two possible values of k.

Answers

$x_1=x_2 \Rightarrow \Delta=0\n\Delta=12^2-4\cdot(3k-2)\cdot3(k+1)\n\Delta=144-(36k-24)(k+1)\n\Delta=144-36k^2-36k+24k+24\n\Delta=-36k^2-12k+168\n-36k^2-12k+168=0\n-3k^2-k+14=0\n-3k^2+6k-7k+14=0\n-3k(k-2)-7(k-2)=0\n-(3k+7)(k-2)=0\nk=-(7)/(3) \vee k=2$

Find the indicated limit, if it exists. (2 points) limit of f of x as x approaches 5 where f of x equals 5 minus x when x is less than 5, 8 when x equals 5, and x plus 3 when x is greater than 5

Answers

It looks like we have

$f(x)=\begin{cases}5-x&\text{for }x<5\n8&\text{for }x=5\nx+3&\text{for }x>5\end{cases}$

and we want to find $\lim\limits_(x\to5)f(x)$ .

Since $x$ is approaching 5, we don't care about the value of $f(x)$ when $x=5$ .

We do care about how $f(x)$ behaves to either side of $x=5$ . If $x\to5$ from below, then $f(x)=5-x$ , so that

$\displaystyle\lim_(x\to5^-)f(x)=\lim_(x\to5)(5-x)=5-5=0$

On the other hand, if $x\to5$ from above, then $f(x)=x+3$ , so that

$\displaystyle\lim_(x\to5^+)f(x)=\lim_(x\to5)(x+3)=5+3=8$

The one-sided limits do not match, since 0 ≠ 8, so the limit does not exist.

Find the solution of the equation 1/2x^2 -x +5=0

Answers

If you would like to solve the equation 1/2 * x^2 - x + 5 = 0, you can do this using the following steps:

1/2 * x^2 - x + 5 = 0 /*2
x^2 - 2x + 10 = 0
(x - 1)^2 + 9 = 0
1. x = 1 - 3 * i
2. x = 1 + 3 * i

The correct result would be x = 1 - 3 * i and x = 1 + 3 * i.

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