Finding the Inverse of a Function: g(x) = x/3 - 5

[Nelo]

Homework Statement

Inverse of g(x) = x/3 -5

Homework Equations

The Attempt at a Solution

The inverse of the function

g(x) = x/3 -5
x= y/3 -5
x +5 = y/ 3
3x + 15 = y

Is this correct?

Or is it x+5 /3 ?

 

[1MileCrash]

Your original looks correct.

If you have a graphic calculator, graph them both, the inverse should be a 90* rotation from the original, since you essentially have the same function with swapped axis.

 

[Averki]

If you want to check to see if the inverse function you found is correct, all you need to do is form a composite function of the original function and its inverse. If the composite function of g(x) and g^-1(x) is equal to x, then the inverse you found is correct.

$g[g^{-1}(x)]=(\frac{3x+15}{3})-5=(x+5)-5=x$

Yes, the inverse you found is correct.