Answered

Consider functions [tex]f[/tex] and [tex]g[/tex]:

[tex]\[
\begin{array}{l}
f(x) = -x^3 \\
g(x) = \left| \frac{1}{8} x - 1 \right|
\end{array}
\][/tex]

What is the value of [tex](g \circ f)(4)[/tex]?

A. -9
B. 9
C. [tex]-\frac{1}{8}[/tex]
D. 1



Answer :

GinnyAnswer
To find the value of [tex]\((g \circ f)(4)\)[/tex], we need to follow a few steps to determine the result.

### Step 1: Calculate [tex]\(f(4)\)[/tex]

Given the function [tex]\(f(x) = -x^3\)[/tex], we need to substitute [tex]\(x = 4\)[/tex] into this function:
[tex]\[ f(4) = -(4)^3 = -64 \][/tex]

So, [tex]\(f(4) = -64\)[/tex].

### Step 2: Calculate [tex]\(g(f(4))\)[/tex]

Next, we use the value obtained from [tex]\(f(4)\)[/tex] as the input for the function [tex]\(g\)[/tex]. The function [tex]\(g(x)\)[/tex] is defined as:
[tex]\[ g(x) = \left| \frac{1}{8}x - 1 \right| \][/tex]

Here, we substitute [tex]\(x = -64\)[/tex] into the function [tex]\(g\)[/tex]:
[tex]\[ g(-64) = \left| \frac{1}{8} \cdot (-64) - 1 \right| \][/tex]

Perform the multiplication first:
[tex]\[ \frac{1}{8} \cdot (-64) = -8 \][/tex]

Then, substitute back into the equation:
[tex]\[ g(-64) = \left| -8 - 1 \right| \][/tex]

Simplify inside the absolute value:
[tex]\[ g(-64) = \left| -9 \right| = 9 \][/tex]

So, [tex]\(g(f(4)) = 9\)[/tex].

### Conclusion

The value of [tex]\((g \circ f)(4)\)[/tex] is [tex]\(\boxed{9}\)[/tex].

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