Define $g$ by $g(x)=5x-4$. If $g(x)=f^{-1}(x)-3$ and $f^{-1}(x)$ is the inverse of the function $f(x)=ax+b$, find $5a+5b$.
First, we find f−1(x) in terms of a and b.
f(x)=ax+bx=af−1(x)+bf−1(x)=x−ba
Now,
g(x)=f−1(x)−35x−4=xa−(ba+3)
Comparing coefficients:
1a=5a=15
5b+3=4b=15
Therefore
5a+5b=5⋅15+5⋅15=2
