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Chapter 1: Problem 27

Evaluate the indicated function for \(f(x)=x^{2}+1\) and \(g(x)=x-4\). $$ (f / g)(-1)-g(3) $$

Short Answer

Expert verified
The result of the expression \((f / g)(-1)-g(3)\) is 0.6.

Step by step solution

01

Evaluate the functions at \(x=-1\)

We substitute \(x=-1\) into both function definitions to get the necessary values. \(f(-1) = (-1)^{2} + 1 = 2\), and \(g(-1) = -1 - 4 = -5\).
02

Apply the division operation

We need to divide \(f(-1)\) by \(g(-1)\), as indicated by the operation \((f/g)(-1)\) in the exercise. So, \( (f/g)(-1) = f(-1) / g(-1) = 2 / -5 = -0.4 \).
03

Evaluate function \(g\) at \(x=3\)

We substitute \(x=3\) into the function g definition to get the necessary value, which is \(g(3) = 3 - 4 = -1\).
04

Perform the subtraction operation

Finally, subtract \(g(3)\) from \((f/g)(-1)\) as required by the exercise. So, \((f / g)(-1)-g(3) = -0.4 - (-1) = 0.6 \).

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