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Chapter 1: Problem 21

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

Short Answer

Expert verified
The evaluation of the function (f-g)(3t) is \(9t^{2} - 3t + 5\).

Step by step solution

01

Note the Provided Functions

Recognize that the two functions that have been provided are \(f(x) = x^{2} + 1\) and \(g(x) = x - 4\).
02

Define (f - g)(x)

The expression '(f - g)(x)' means to subtract function \(g(x)\) from function \(f(x)\). To do this, subtract the formula for \(g(x)\) from the formula for \(f(x)\). The resulting function is \(h(x)=f(x)-g(x)=x^{2} + 1 - (x - 4)=(x^{2} + 1 - x + 4)\). This simplifies to \(h(x)= x^{2} - x + 5\).
03

Evaluate (f - g)(3t)

We now evaluate \(h(x)\) for \(x = 3t\). Plugging this into our function gives \(h(3t) = (3t)^{2} - 3t + 5 = 9t^{2} - 3t + 5\).

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Most popular questions from this chapter

On a yardstick with scales in inches and centimeters, you notice that 13 inches is approximately the same length as 33 centimeters. Use this information to find a mathematical model that relates centimeters \(y\) to inches \(x\). Then use the model to find the numbers of centimeters in 10 inches and 20 inches.

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