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Use substitution to compose the two functions: [tex]p = 9q^9[/tex] and [tex]D = 8p - 3[/tex].

[tex]D = \square[/tex]

Sagot :

To compose the two functions [tex]\( p \)[/tex] and [tex]\( D \)[/tex] using substitution, follow these steps:

1. Define the Function [tex]\( p \)[/tex]:
The function [tex]\( p \)[/tex] is given by:
[tex]\[ p(q) = 9 q^9 \][/tex]

2. Define the Function [tex]\( D \)[/tex]:
The function [tex]\( D \)[/tex] is given by:
[tex]\[ D(p) = 8p - 3 \][/tex]

3. Substitute [tex]\( p(q) \)[/tex] into [tex]\( D(p) \)[/tex]:
We need to express [tex]\( D \)[/tex] in terms of [tex]\( q \)[/tex] by substituting the expression for [tex]\( p \)[/tex] into the function [tex]\( D \)[/tex].

Start with the function [tex]\( D \)[/tex]:
[tex]\[ D(p) = 8p - 3 \][/tex]

Substitute [tex]\( p(q) = 9 q^9 \)[/tex] into this equation:
[tex]\[ D(p(q)) = 8(9 q^9) - 3 \][/tex]

Simplify the expression inside the parentheses:
[tex]\[ D(p(q)) = 72 q^9 - 3 \][/tex]

4. Write the Final Composed Function:
The composed function [tex]\( D \)[/tex] in terms of [tex]\( q \)[/tex] is:
[tex]\[ D = 72 q^9 - 3 \][/tex]

So, the composed function [tex]\( D \)[/tex] is:
[tex]\[ D = 72 q^9 - 3 \][/tex]

Therefore, by substitution, we have:
[tex]\[ D = 72 q^9 - 3 \][/tex]