Question

The graph shows the function f(x) = 6(3)x. What is the value of the inverse function, f −1, at x = 2?

Answer 1

There is an error in the equation.

f ( x ) = 63 X?? or whatt??

Answer 2

-1

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.