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UNO [17]
3 years ago
6

PLEASE SHOW YOUR WORK!!! Solve for y: 3^3 + 14 y- (25y - 13) = y + 7y - 9y

Mathematics
1 answer:
Marina86 [1]3 years ago
6 0
<h2 /><h2>⟹</h2>

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

3^3+14*y-(25*y-13)-(y+7*y-9*y)=0

Equation at the end of step 1

((3³ + 14y) - (25y - 13)) - -y = 0

Pull out like factors :

40 - 10y = -10 • (y - 4)

Equation at the end of step3:

-10 • (y - 4) = 0

STEP4:

Equations which are never true:

Solve : -10 = 0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation:

Solve : y-4 = 0

Add 4 to both sides of the equation :

y = 4

<h2>y = 4</h2>

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Find the equation of the inverse.<img src="https://tex.z-dn.net/?f=y%20%3D%20%20%7B2%7D%5E%7Bx%20%2B%205%7D%20%20-%206" id="TexF
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Find the equation of the inverse.

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we have

y=\mleft\{2\mright\}^{\mleft\{x+5\mright\}}-6

step 1

Exchange the variables

x for y and y for x

x=\{2\}^{\{y+5\}}-6

step 2

Isolate the variable y

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apply log both sides

\begin{gathered} \log (x+6)=(y+5)\cdot\log (2) \\ y+5=\frac{\log (x+6)}{\log (2)} \\  \\ y=\frac{\log(x+6)}{\log(2)}-5 \end{gathered}

step 3

Let

f^{(-1)}(x)=y

therefore

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f^{(-1)}(x)=\frac{\log(x+6)}{\log(2)}-5

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