# Thread: linear functions and their inverse.

1. ## linear functions and their inverse.

how do i solve this problem?

Find the linear function f with x-intercept 6 and f -1 (-8) = -3.

i don't know how to do this at all.

2. Are you in a course where you are expected to be able to do that? If so, do you know what a "linear function" is? Do you know any formulas for linear functions?

3. y=mx+b?

4. Originally Posted by FinalFantasy9291
y=mx+b?
Now use the given information, "with x-intercept 6" to get an equation with m and b in it. Call this equation (1).

Do you know anything about inverse functions? If so, then you should know that if (-8, -3) lies on the graph of $\displaystyle y = f^{-1}(x)$, then (-3, -8) lies on the graph of y = f(x). Use this to get another equation with m and b in it. call this equation (2).

Now solve equations (1) and (2) simultaneously for m and b.

5. Originally Posted by FinalFantasy9291
y=mx+b?
Great! Of course, to give a specific function, you need to know m and b- two values.

Also, you know f(6)= 0 and that f(-3)= -8. (Do you see why?) Set x= 6, y= 0 and then x= -3, y= -8 into y= mx+ b to get two equations to solve for m and b.