f(x) = ax+b, a and b are real constants, and g(x) = 2x - 5. Suppose that for all x, it is true that g(f(x)) = 3x + 4. What is a+b?

g(f(x)) = 2(f(x)) - 5 = 2(ax + b) - 5 = 2ax + 2b - 5

Compare coefficients of x with 3x + 4

so 2a = 3

and 2b - 5 = 4

I'll leave you to complete this.