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2 years ago

Find the inverse of f(x) = -6xˆ2 + 24x - 100

Mathematics

1 answer:

monitta2 years ago

5 0

Answer:

See below

Step-by-step explanation:

y = -6x^2 + 24x-100

solve for 'x'

y + 100 = -6x^2 + 24x = -6(x^2-4x) complete the square for x

(y+100) /(-6 ) = (x-2)^2 -4 add 4 to both sides

(y+100)/(-6) +4 = (x-2)^2 sqrt both sides

sqrt [ ( y+100)/(-6) + 4 ] + 2 = x change x and y

y = ± sqrt [ (x+100)/(-6) + 4 ] + 2 simplify (if needed)

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Solve the following system by any method -8x-8y=0 -8x+2y=-20

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$\fbox{Solution by using Matrix}$

$\text{Linear Equation} = -8x-8y=0 , -8x+2y=-20$

$\text{Rewrite the linear equations above as a matrix}$

$\left[\begin{array}{ccc}8&-8&0\\-8&2&-20\\\end{array}\right]$

$\text{Apply to Row2 : Row2 + Row1}$

$\left[\begin{array}{ccc}8&-8&0\\-8&-6&-20\\\end{array}\right]$

$\text{ Simplify rows}$

$\left[\begin{array}{ccc}8&-8&0\\0&1&10/3\\\end{array}\right]$

$\text{Note: The matrix is now in echelon form.}$ $\text{The steps below are for back substitution.}$

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$\left[\begin{array}{ccc}8&0&80/30\\0&1&10/3\\\end{array}\right]$

$\text{ Simplify rows}$

$\left[\begin{array}{ccc}1&0&10/3\\0&1&10/3\\\end{array}\right]$

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$x= \dfrac{10}{3} \ \text{and} \ \ y=\dfrac{10}{3}$

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