Answer:
g(0)⁻¹ = 6
Explanation:
First, you must find the inverse of the function. Remember, another way of representing g(x) is with "y". To find the inverse, you must swap the positions of the "x" and "y" variables in the equation. Then, you must rearrange the equation and isolate "y".
g(x) = 18 - 3x <----- Original function
y = 18 - 3x <----- Plug "y" in for g(x)
x = 18 - 3y <----- Swap the positions of "x" and "y"
x + 3y = 18 <----- Add 3y to both sides
3y = 18 - x <----- Subtract "x" from both sides
y = (18 - x) / 3 <----- Divide both sides by 3
y = 6 - (1/3)x <----- Divide both terms by 3
Now that we have the inverse function, we need to plug x = 0 into the equation and solve for the output. In the inverse function, "y" is represented by the symbol g(x)⁻¹.
g(x)⁻¹ = 6 - (1/3)x <----- Inverse function
g(0)⁻¹ = 6 - (1/3)(0) <----- Plug 0 in for "x"
g(0)⁻¹ = 6 - 0 <----- Multiply 1/3 and 0
g(0)⁻¹ = 6 <----- Subtract