The graph shows the function f(x) = 6(3)^x What is the value of the inverse function, f ^-1 at x = 2​

Step-by-step explanation:

y = f(x)

y = 6 * 3^x

Interchange x and y

x = 6 * 3^y

Divide by 6

x/6 = 3^y  

Take the log of both sides

log(x/6) = log(3)^y

Bring the y down

log(x/6) = y log(3)                   \

Divide by log(3)

log(x/6)/log(3) = y

Let x = 2

log(2/6) / log(3) = y

-(0.4771 )/ 0.4771 = y

y = - 1

Remark

The original graph is in green

The red graph is the inverse.

The point (2,-1) is marked so that you know it falls on the inverse.

goog may have it for you

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.