Answer: x^2-2x+8
Step-by-step explanation:
its does not factor any more
its already in its lest form so therefore
the answer is x^2-2x+8
Hope this helps :)
I'm not sure what is meant by "partitioning the <em>x</em>-axis" - partition is a term more often used with computing Riemann sums. So either partitioning has a special meaning for you, or you have to approximate the area with a Riemann sum.
I'm going to assume you just want the exact area of the given region. Notice that the two curves <em>y</em> = 4<em>e</em> ˣ and <em>y</em> = -<em>x</em> + 4 intersect when <em>x</em> = 0 at the point (0, 4). Both curves then meet the vertical line <em>x</em> = 4. The exponential function is increasing while the linear one is decreasing, so 4<em>e</em> ˣ ≥ -<em>x</em> + 4.
The region is then the set of points,
<em>R</em> = {(<em>x</em>, <em>y</em>) | 0 ≤ <em>x</em> ≤ 4 and -<em>x</em> + 4 ≤ <em>y</em> ≤ 4<em>e</em> ˣ}
so the area is given by the integral,
Answer:
Step-by-step explanation:
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The answer is: [C]: " f ⁻¹(x) = (5x + 3) / 2 " .
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Explanation:
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Given: "f(x) = (2x - 3) / 5 ; which is the "inverse" of: " f(x)" ?
Substitute "y" for "f(x)" :
y = (2x - 3) / 5 ;
Replace "x" with "y"; and "y" with "x" ; and rewrite:
x = (2y - 3) / 5 ;
Now, solve for "y" , in term of "x' ;
Multiply each side of the equation by "5"
5 * x = 5 * { (2y - 3) / 5 } ;
to get:
5x = 2y - 3 ;
Add "3" to each side of the equation:
5x + 3 = 2y - 3 + 3 ;
to get: 5x + 3 = 2y ;
↔ 2y = 5x + 3 ;
Divide each side of the question by "2" ;
to isolate "y" on one side of the equation; & to solve for "y" in terms of "x" ;
→ 2y / 2 = (5x + 3) / 2 ;
to get: y = (5x + 3) / 2 ;
Replace the "y" with: " f ⁻¹(x) " ;
and rewrite:
" f ⁻¹(x) = (5x + 3) / 2 " ;
→ which is: "Answer choice: [C]: " f ⁻¹(x) = (5x + 3) / 2 " .
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Answer:
72
Step-by-step explanation: