Find the inverse function in slope-intercept form (mx+b):

Question

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

Answer 1

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.