what is the inverse of g(x)= 2/3x+4?
g(x) = (2/3)x + 4
or
y = (2/3)x + 4
inverse :
x = (2/3)y + 4
3x = 2y + 12
2y = 3x - 12
y = (3/2)x - 6
test:
g(6) = (2/3)(6) + 4
= 8
g^-1(8) = (3/2)(8) - 6
= 12-6 = 6
my answer is correct
To find the inverse of a function, you need to interchange the x and y variables and solve for y. Let's do that for the given function g(x) = (2/3)x + 4.
Step 1: Replace g(x) with y:
y = (2/3)x + 4
Step 2: Interchange x and y:
x = (2/3)y + 4
Step 3: Solve for y:
First, subtract 4 from both sides:
x - 4 = (2/3)y
Next, multiply both sides by 3/2 (or divide by 2/3) to isolate y:
y = (3/2)(x - 4)
Hence, the inverse of g(x) = (2/3)x + 4 is f(x) = (3/2)(x - 4).
Therefore, the inverse function is f(x) = (3/2)(x - 4).