Find the inverse function in slope-intercept form (mx+b):
f, left bracket, x, right bracket, equals, minus, start fraction, 4, divided by, 3, end fraction, x, minus, 16
f(x)=
−
3
4
x−16
To find the inverse function, we start by swapping the x and y variables and then solving for y.
So, starting with the equation: y = -4/3x - 16
Swap x and y: x = -4/3y - 16
Now, solve for y:
x + 16 = -4/3y
To get y alone, multiply both sides by -3/4:
(-3/4)(x + 16) = y
Now, simplify:
y = -3/4x - 12
Therefore, the inverse function of f(x) = -4/3x - 16 is f^(-1)(x) = -3/4x - 12.