The inverse of f(x) is h(x). The composition of f and h is written f[h(x)]. What does f[h(x)] equal?
Hint: Think of a simple problem like f(x) = x + 3. Then the inverse, h(x) would be h(x) = x - 3. What would the composition f[h(x)] equal in this example?
f(h) means the function operates on h.
f(h)= h+3= x-3+3=x
Notice that
h(f)= f-3=x=3-3=x
To find the value of f[h(x)], we need to substitute the expression h(x) into the function f(x).
In the given example, f(x) = x + 3 and h(x) = x - 3.
To find f[h(x)], substitute h(x) into f(x):
f[h(x)] = f(x - 3)
Now we can plug in the expression for h(x) into f(x):
f[h(x)] = f(x - 3) = (x - 3) + 3
Simplifying, we get:
f[h(x)] = (x - 3) + 3 = x
So in this example, f[h(x)] equals x.
This means that when we apply the composition of f and h, the output will always be the same as the input value.