teach me---. Linear Function
A function is defined as f(x) = 3x - 7.
What is the value of f(4)?
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Let's solve this linear function problem step by step. We have the function f of x equals 3x minus 7, and we need to find f of 4. This means we substitute x equals 4 into our function.
Now let's work through the substitution step by step. First, we write our original function. Then we substitute x equals 4 into the function, giving us f of 4 equals 3 times 4 minus 7. Next, we multiply 3 times 4 to get 12, so we have f of 4 equals 12 minus 7. Finally, we subtract to get our answer: f of 4 equals 5.
Let's break down the calculation in detail. We start with f of 4 equals 3 times 4 minus 7. First, we perform the multiplication: 3 times 4 equals 12. This gives us f of 4 equals 12 minus 7. Then we perform the subtraction: 12 minus 7 equals 5. Therefore, our final answer is f of 4 equals 5.
Let's verify our answer and understand the concept better. We found that f of 4 equals 5, which means the point (4, 5) lies on our linear function. Linear functions have the form f of x equals mx plus b, where m is the slope and b is the y-intercept. In our function f of x equals 3x minus 7, the slope is 3 and the y-intercept is negative 7. This confirms our calculation is correct.
To summarize what we've learned: We successfully evaluated f of 4 for the linear function f of x equals 3x minus 7. Through substitution, we found that f of 4 equals 5, which represents the point (4, 5) on the line. This demonstrates the fundamental process of function evaluation, which is an essential skill in algebra and mathematics.