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bixtya [17]
1 year ago
10

Find the Inverse Function : Algebra 2y = 2x² + 1​

Mathematics
1 answer:
Vera_Pavlovna [14]1 year ago
3 0

\displaystyle\\Answer:\ y=\sqrt{\frac{x-1}{2} }  \ \ \ \ (x\geq 1,\ \ \ \ y\geq 0)

Step-by-step explanation:

y=2x^2+1\\

<em>We change the argument and the value:</em>

\displaystyle\\x=2y^2+1\\\\x-1=2y^2+1-1\\\\x-1=2y^2\\

<em>Divide both parts of the equation by 2:</em>

\displaystyle\\\frac{x-1}{2}=y^2\\\\ \sqrt{\frac{x-1}{2} }=y \  -\  the\  desired\  inverse\  function\\\\

<em>The restrictions are imposed on the inverse function by on x:</em>

x-1\geq 0\\x\geq 1

<em>The restrictions are imposed on the inverse function by on y:</em>

y\geq 0

<em>Then the original function is defined on the sets:</em>

x\geq 1,\ \ \ \ y\geq 0

<em>The initial function, a parabola, is constrained because of the inverse function; only in this case the functions are reciprocal.</em>

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Vikentia [17]

Answer:

The answer is:

y =  \frac{1}{3} x -  \frac{5}{3}

Step-by-step explanation:

❃Incase you forgot what the linear equation formula is ☟

y = mx + b

❃Incase you also forgot, The is what the slope formula is ☟

m = \frac{y_2 - y_1 }{x_2 - x_1}

➊ First: We are going to be solving for the slope.

m = \frac{  - 5 - 0}{ - 10 - 5} = \frac{ - 5}{  - 15} =  \frac{1}{3}

➋Second: We find the y-intercept.

y = mx + b \\ 0 =  \frac{1}{3} (5) + b \\ 0 =  \frac{5}{3}  + b \\ \frac{  -   \frac{5}{3}  =  -  \frac{5}{3 }   \:  \:  \:  \:  \:  \:  \: \: \: \: \: \: }{  -  \frac{5}{3}  = b}

➌Third: Plug in.

y =  \frac{1}{3} x -  \frac{5}{3}

4 0
3 years ago
How do you write -1.838383
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An item sells for $30 and is on sale for 15% off and the sales tax is 8.2%. What is the final cost to the nearest cent?
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Answer:

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Step-by-step explanation:

1) First we calculate the sales tax:

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2) Now we calculate sales tax

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25.5 + 2.09 = $27.59

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Answer:

Step-by-step explanation:

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Please help me with this.
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