Let f(x) = 3x + 4 and g(x) = 2x + 8. If h(x) = f(g(x)) , then what is the inverse of h(x)?
+21 Let us simplify h(x) first. Plugging in the value of g(x) directly into h(x), we get:
h(x) = f(2x + 8)
We then can plug in 2x + 8 into f(x), to get:
h(x) = 3(2x + 8) + 4
h(x) = 6x + 28
In order to find the inverse of a function, we have to switch the x and y values first. Hence, we get:
y = 6x + 28
x = 6y + 28
We then have to solve for y. Solving for y, we get:
x - 28 = 6y
(x-28)/6 = y
Therefore, the inverse function of h(x) is \(h^{-1}(x) = \frac{x-28}{6}\)
