+4609 The graphs of a function \(f(x)=3x+b\) and its inverse function \(f^{-1}(x)\) intersect at the point \((-3,a)\) . Given that b and a are both integers, what is the value of \(a\)?
+128407 The inverse function is
y = [x - b] / 3
Set these functions equal
3x + b = [x - b]/ 3
9x + 3b = x - b
8x = -4b
b = -2x
So...using the first function
y = 3x - 2x
a = 3(-3) - 2(-3)
a = -9 + 6
a = -3 and b = -2(-3) = 6
Check
y = 3(x) + 6 and y = [ x - 6 ] / 3
a = 3(-3) + 6 -3 = [ a - 6] / 3
a = -3 -3 = [ -3 - 6] / 3
-3 = [-9] / 3
-3 = -3
So....the intersection point is (-3, -3)
See the graph here : https://www.desmos.com/calculator/r2jbhnwsj2
