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Answer :
Final answer:
To compute (f∘g)(x) with f(x)=7x⁶ and g(x)=9x-4, you substitute g(x) into f(x) leading to f(9x - 4). The correct answer after composition and simplification is option a) 63x⁶-28.
Explanation:
To find the composition \( (f \circ g)(x) \) of the function \( f(x) = 7x^6 \) with \( g(x) = 9x - 4 \), we substitute \( g(x) \) into \( f(x) \) wherever there is an \( x \). So, we will evaluate \( f(g(x)) \).
The result will be \( f(g(x)) = f(9x - 4) \), which means we need to plug \( 9x - 4 \) into \( f(x) \) wherever we see an \( x \). Therefore, we get:
\[ f(9x - 4) = 7(9x - 4)^6 \]
Since it's given that \( (x^a)^b = x^{a.b} \), we need to first expand \( (9x - 4)^6 \) as \( 9x - 4 \) six times multiplied together, but for this example, we will not expand it fully as it's not necessary to find the coefficient terms.
Instead, we know that the first term of the expansion will be \( (9x)^6 = 9^6x^6 \) and that multiplying this by \( 7 \) gives us the term \( 7 \times 9^6x^6 \). This is \( 7 \times 9^6 \) times \( x^6 \), or \( 63x^6 \) as the base term of the expansion, because \( 9^6 = 9 \times 9 \times 9 \times 9 \times 9 \times 9 \) and the rule given is \( (xa)^b = xa.b \).
Therefore, the only option which correctly starts with \( 63x^6 \) is:
a) 63x^6 - 28
Please mention the correct option in the final answer. The correct option here is a) 63x^6 - 28.
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