The value of g(x) is 8x³ - 1 given that f(x) is (8x³ - 1)³, h(x) is x³ and f(x) = (h ° g) (x). This can be obtained by finding composite of (h ° g) (x) using the formula for composition.
Find the value of g(x):
Composition of a function : A composite function is created when one function is substituted into another.
f composite of g is denoted as (f ° g)
The formula to find the composite of a function,
For example,
f(x) = x + 2, and g(x) = 3x
- (f ° g)(x) = f(g(x)) = g(x) + 2 = 3x +2
- (g ° f)(x) = g(f(x)) = 3(f(x)) = 3(x+2) = 3x + 6
In the question,
Given that, f(x) = (8x³ - 1)³, h(x) = x³
f(x) = (h ° g) (x)
⇒ (8x³ - 1)³ = h(g(x))
⇒ (8x³ - 1)³ = (g(x))³
Taking cube roots on both sides,
⇒ ∛(8x³ - 1)³ = ∛(g(x))³
⇒ (8x³ - 1) = (g(x))
⇒ g(x) = 8x³ - 1
Hence the value of g(x) is 8x³ - 1 given that f(x) is (8x³ - 1)³, h(x) is x³ and f(x) = (h ° g) (x).
Learn more about composite of a function here:
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