The value of (f - g)(x) is -x² + 3x + 7.
<h3>What is Function?</h3>
The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Here, the given functions are;
f(x) = 3x + 1
g(x) = x² - 6
Now,
(f - g)(x) = f(x) - g(x)
= (3x + 1) - (x² - 6)
= 3x + 1 - x² + 6
(f - g)(x) = -x² + 3x + 7
Thus, the value of (f - g)(x) is -x² + 3x + 7.
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The speed of plane is 105 miles per hour and speed of wind is 28 miles per hour.
Step-by-step explanation:
Given,
The distance traveled by plane = 1463 miles
The trip with the wind took 11 hours.
The trip took 19 hours against the wind.
Let,
s be the speed of plane and w be the speed of wind.
Therefore;
Speed with the wind = s+w
Speed into the wind = s-w
We know that;
Distance = Speed * Time
Therefore;
Equation for trip taken with wind.
1463 = 11(s+w)
Dividing both sides by 11

Equation for trip taken into the wind
1463 = 19(s-w)
Dividing both sides by 19

Adding Eqn 1 and 2

Dividing both sides by 2

Putting s=105 in Eqn 1

The speed of plane is 105 miles per hour and speed of wind is 28 miles per hour.