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gulaghasi [49]
3 years ago
10

Given that g(x)=3x²-5x+7 find the following: g(-x)

Mathematics
1 answer:
AURORKA [14]3 years ago
5 0
G(x) = 3x² - 5x + 7
g(-x) = -(3x² - 5x + 7)
g(-x) = -3x² + 5x - 7

This equation cannot be solved because of a few reasons,

1. This equation didn't show that it equals to 0.
2. Even if it equals to zero, square root of a negative number cannot be solved.
(I will show you what I mean)

-3x² + 5x - 7
is the same as
3x² - 5x + 7
by shifting the equation,

for example,
1 - 3 = -2
shifting other side
2 = -1 + 3

using 3x² - 5x + 7 to solve,

Solve\ using\ the\ formular\ \ \boxed{ x= { \frac{-b \pm \sqrt{b^2-4ac} }{2a} } }
a = 3
b = -5
c = 7
x= { \frac {-(-5) \pm \sqrt{ (-5)^2-4(3)(7) } }{2(3)} }
x= { \frac {5 \pm \sqrt{-59} }{6} }

∴This equation cannot be solved.
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Use the definition of continuity and the properties of limit to show that the function f(x)=x sqrtx/ (x-6)^2 is continuous at x=
jasenka [17]

Answer:

The function \\ f(x) = \frac{x*\sqrt{x}}{(x-6)^{2}} is continuous at x = 36.

Step-by-step explanation:

We need to follow the following steps:

The function is:

\\ f(x) = \frac{x*\sqrt{x}}{(x-6)^{2}}

The function is continuous at point x=36 if:

  1. The function \\ f(x) exists at x=36.
  2. The limit on both sides of 36 exists.
  3. The value of the function at x=36 is the same as the value of the limit of the function at x = 36.

Therefore:

The value of the function at x = 36 is:

\\ f(36) = \frac{36*\sqrt{36}}{(36-6)^{2}}

\\ f(36) = \frac{36*6}{900} = \frac{6}{25}

The limit of the \\ f(x) is the same at both sides of x=36, that is, the evaluation of the limit for values coming below x = 36, or 33, 34, 35.5, 35.9, 35.99999 is the same that the limit for values coming above x = 36, or 38, 37, 36.5, 36.1, 36.01, 36.001, 36.0001, etc.

For this case:

\\ lim_{x \to 36} f(x) = \frac{x*\sqrt{x}}{(x-6)^{2}}

\\ \lim_{x \to 36} f(x) = \frac{6}{25}

Since

\\ f(36) = \frac{6}{25}

And

\\ \lim_{x \to 36} f(x) = \frac{6}{25}

Then, the function \\ f(x) = \frac{x*\sqrt{x}}{(x-6)^{2}} is continuous at x = 36.

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Fofino [41]

Answer:

x = 25

Step-by-step explanation:

2/5x - 1 = 9

Add 1 to both sides

2/5x = 10

Multiply by 5 on both sides

2x = 50

Divide by 2 on both sides

x = 25

Check the answer:

Plug in 25 for x

2/5(25) - 1 = 9

10 - 1 = 9

9 = 9

The answer is correct.

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