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3 f(x)=(3x−5) 3 f, left parenthesis, x, right parenthesis, equals, left parenthesis, 3, x, minus, 5, right parenthesis, cubed h ( x ) = 2 x 3 + 8 h(x)=2 3 x ​ +8h, left parenthesis, x, right parenthesis, equals, 2, cube root of, x, end cube root, plus, 8 Write h ( f ( x ) ) h(f(x))h, left parenthesis, f, left parenthesis, x, right parenthesis, right parenthesis as an expression in terms of x xx. h ( f ( x ) ) = h(f(x))=h, left parenthesis, f, left parenthesis, x, right parenthesis, right parenthesis, equals

Answer :

abidemiokin

Answer:

[tex]h(f(x)) = 18x -22[/tex]

Step-by-step explanation:

Given

f (x) = [tex](3x-5)^3[/tex]

[tex]h(x) =2\sqrt[3]{3x} + 8[/tex]

We are to find the composite function [tex]h(f(x))[/tex]

[tex]h(f(x))[/tex][tex]= h ((3x-5)^3)[/tex]

To get [tex]h ((3x-5)^3)[/tex], we will substitute x as (3x-5)³ in h(x)as shown:

[tex]h(x) =2\sqrt[3]{3(3x-5)^3} + 8\\h(f(x)) =2(3(3x-5)+ 8\\h(f(x)) = 2(9x-15)+8\\h(f(x)) =18x-30+8\\h(f(x)) = 18x - 22[/tex]

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