What is the inverse of y= 10^x +8?

, where .

Step-by-step explanation:

The question is asking for an expression for in terms of .

The first step is to move as many constants away from the side with as possible. In this question, that could be done by subtracting from both sides of the equation.

.

.

Notice how is in the position of an exponent. Logarithms could help move out of that position.

For any base :

.

In this question, would be the base. That is: .

Take the logarithm (with as the base) of both sides of the equation :

Equate both sides to find an expression for :

.

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

tap for more

y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation:

the correct answer is x/3+10≥32

hope this !