Which equation is the inverse of (x-4)^2-2/3=6y-12

Answer-

Solution-

The given function,

The inverse of a function normally means switching the role of the variables. ( y becomes the input or independent variable, and x becomes the output or the dependent variable)

Switching x and y, the function becomes,

The inverse of a function is its opposite

The inverse of the equation is y = 4 + 18x-34

The equation is given as:

(x-4)^2-2/3=6y-12

Swap the positions of x and y

(y-4)^2-2/3=6x-12

Multiply through by 3

(y-4)^2-2=18x-36

Add 2 to both sides

(y-4)^2=18x-34

Take the square roots of both sides

y-4=18x-34

Add 4 to both sides

y = 4 + 18x-34

Hence, the inverse of the equation is y = 4 + 18x-34

Read more about inverse equations at:

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x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752