f(x)=x^(3)-6 h(x)=root(3)(2x-15) Write f(h(x)) as an expression in terms of x. f(h(x))=

Identify functions and question: First, we need to identify the functions given and what is being asked. We have two functions: f(x) = x^3 - 6 h(x) = ³√(2x - 15) We are asked to find the composition of these functions, which is f(h(x)).Substitute h(x) into f(x): To find f(h(x)), we need to substitute the expression for h(x) into the function f(x) wherever there is an x. So, we will replace x in f(x) with ³√(2x - 15).Perform the substitution: Now, we perform the substitution: f(h(x)) = (³√(2x - 15))^3 - 6Simplify the expression: Next, we simplify the expression. When we raise a cube root to the power of 3, they cancel each other out, so we are left with: f(h(x)) = (2x - 15) - 6Combine like terms: Finally, we simplify the expression by combining like terms: f(h(x)) = 2x - 15 - 6 f(h(x)) = 2x - 21

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f(x)=x^(3)-6

h(x)=root(3)(2x-15)
Write
f(h(x)) as an expression in terms of
x.

f(h(x))=

$f(x)=x^{3}-6$ $\newline$ $h(x)=\sqrt[3]{2 x-15}$ $\newline$ Write $f(h(x))$ as an expression in terms of $x$ . $\newline$ $f(h(x))=$

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Algebra 1

Compare linear and exponential growth

Full solution

f(x)=x^{3}-6

\newline

h(x)=\sqrt[3]{2 x-15}

\newline

Write

f(h(x))

as an expression in terms of

x

\newline

f(h(x))=

Identify functions and question: First, we need to identify the functions given and what is being asked. We have two functions: $\newline$ $f(x) = x^3 - 6$ $\newline$ $h(x) = \sqrt[3]{2x - 15}$ $\newline$ We are asked to find the composition of these functions, which is $f(h(x))$ .
Substitute $h(x)$ into $f(x)$ : To find $f(h(x))$ , we need to substitute the expression for $h(x)$ into the function $f(x)$ wherever there is an $x$ . So, we will replace $x$ in $f(x)$ with $\sqrt[3]{2x - 15}$ .
Perform the substitution: Now, we perform the substitution: $f(h(x)) = (\sqrt[3]{2x - 15})^3 - 6$
Simplify the expression: Next, we simplify the expression. When we raise a cube root to the power of $3$ , they cancel each other out, so we are left with: $\newline$ $f(h(x)) = (2x - 15) - 6$
Combine like terms: Finally, we simplify the expression by combining like terms: $\newline$ $f(h(x)) = 2x - 15 - 6$ $\newline$ $f(h(x)) = 2x - 21$