Evaluate h(3), where h = g compose f.
f(x) = cubert.(x^2 − 9) g(x) = 8x^3 + 9
g(x) = 8x³+9
f(x) = (x²-9)^(1/3)
h(x)
= g o f
= g(f(x))
= g((x²-9)^(1/3)
= 8((x²-9)^(1/3))³+9
= 8(x²-9)+9
h(3)
= 8(3²-9)+9
= 8(0)+9
= 9
[CUBERT(2x + 9)]=3
To evaluate h(3), we need to find the composition of g and f and then substitute 3 into the resulting expression.
First, let's find the composition of g and f. The composition of two functions, denoted as (g compose f)(x), is given by g(f(x)). In other words, we substitute f(x) into the function g.
Given f(x) = cubert.(x^2 − 9) and g(x) = 8x^3 + 9, we can find h(x) = (g compose f)(x) as follows:
h(x) = g(f(x))
h(x) = g(cubert.(x^2 − 9))
Next, we need to evaluate h(3) by substituting x = 3 into the expression we derived for h(x):
h(3) = g(cubert.(3^2 − 9))
h(3) = g(cubert.(9 − 9))
h(3) = g(cubert.(0))
Therefore, in order to calculate h(3), we need to evaluate the function g at the value of cubert.(0).
Calculating cubert.(0), we find:
cubert.(0) = 0
Now, substituting cubert.(0) into the function g(x) = 8x^3 + 9, we can find h(3):
h(3) = g(0)
h(3) = 8(0)^3 + 9
h(3) = 0 + 9
h(3) = 9
Therefore, h(3) = 9.