i have attached this problem
Hello,
if
h(x) = x³
f(x) = x-1
g(x) = 2x
Then you get the required function:
1. Plug in the term of f(x) into h: $\displaystyle h(f(x)) = (x-1)^3$
2. Now plug in this term into g:
$\displaystyle g(h(f(x))) = 2 \cdot (x-1)^3$
To calculate the equation of the inverse function you change the x and y-values:
$\displaystyle y = 2(x-1)^2 ~ \Longrightarrow ~ x = 2(y-1)^2$ . Now solve for y and you'll get:
$\displaystyle y = 1 + \sqrt[3]{\frac{1}{2} x}$
1. The graph of the inverse function is the inflection of the graph of the function at the line y = x
2. Therefore the graph of the inverse function and the original function intersect on the line y = x (if there are any intersections, of course)
3. The zeros of the original function are the y-intercepts of the inverse function; The y-intercepts of the original function are the zeros of the inverse function.