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Chapter 1: Problem 30

Evaluate the function for the indicated values. \(g(x)=-7[x+4]+6\) (a) \(g\left(\frac{1}{8}\right)\) (b) \(g(9)\) (c) \(g(-4)\) (d) \(g\left(\frac{3}{2}\right)\)

Short Answer

Expert verified
\[g\left(\frac{1}{8}\right)=-22.875\], \[g(9)=-69\], \[g(-4)=34\], \[g\left(\frac{3}{2}\right)=-34.5\]

Step by step solution

01

Substitute \(x\) with \(\frac{1}{8}\)

Replace \(x\) in \(g(x)=-7[x+4]+6\) with \(\frac{1}{8}\). This gives \(g\left(\frac{1}{8}\right)=-7\left[\frac{1}{8}+4\right]+6\).
02

Simplify \(\frac{1}{8}+4\)

Solving inside the bracket first we get \(g\left(\frac{1}{8}\right)=-7[4.125]+6\).
03

Multiply by -7 and then add 6

Perform the operations in the given order and we get \(g\left(\frac{1}{8}\right)=-28.875+6\).
04

Simplify

Performs the addition to get \(g\left(\frac{1}{8}\right)=-22.875\).
05

Repeat Steps 1 to 4 for the remaining values

Repeat the steps for \(x=9\), \(x=-4\), \(x=\frac{3}{2}\). The results are \(g(9)=-69\), \(g(-4)=34\), \(g\left(\frac{3}{2}\right)=-34.5\).

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