Question

F(x)=(3x-5)^3f(x)=(3x−5) 3 f, left parenthesis, x, right parenthesis, equals, left parenthesis, 3, x, minus, 5, right parenthesis, cubed h(x)=2\sqrt[3]{x}+8h(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 xxx.

Answer 1

Answer:

$h(f(x)) =6x-2$

Step-by-step explanation:

Given

$f(x) = (3x-5)^3\\h(x) = 2\sqrt[3]{x}+8$

Required

Write $h(f(x))$ in terms of x

$h(f(x)) = h((3x-5)^3)$

To get $h((3x-5)^3)$, we will replace x in h(x) with (3x-5)³ as shown:

$h((3x-5)^3) = 2\sqrt[3]{(3x-5)^3} +8\\ h((3x-5)^3) = 2(3x-5) + 8\\ h((3x-5)^3) = 6x - 10 + 8\\ h((3x-5)^3) = 6x-2\\Hence \ h(f(x)) =6x-2$

Hence the expression $h(f(x))$ in terms of x is 6x - 2