Final answer:
The inverse of the function f(x) = 3/4x - 15/4 in slope-intercept form is y = x + 5. The process involves swapping x and y, solving for y, and ensuring the result is in y = mx + b format, where m is the slope and b is the y-intercept.
Step-by-step explanation:
To find the inverse of a function, first you must replace f(x) with y, and then swap x and y. The function you provided is f(x) = \(\frac{3}{4}\)x - \(\frac{15}{4}\). Let's find its inverse step by step:
- Replace f(x) with y: y = \(\frac{3}{4}\)x - \(\frac{15}{4}\).
- Swap x and y: x = \(\frac{3}{4}\)y - \(\frac{15}{4}\).
- Solve for y: First, add \(\frac{15}{4}\) to both sides to get x + \(\frac{15}{4}\) = \(\frac{3}{4}\)y.
- Then multiply both sides by \(\frac{4}{3}\) to get \(\frac{4}{3}\)(x + \(\frac{15}{4}\)) = y.
- Simplify to find the inverse function: y = x + 5, which is your inverse function in slope-intercept form.
It's important to note that the slope-intercept form is represented as y = mx + b, where m is the slope and b is the y-intercept.