wo functions are shown below.f(x) = 12 • 2xg(x) = 5x + 2What is the largest integer value of x such that f(x) ≤ g(x)?
Question
What is the largest integer value of x such that f(x) ≤ g(x)?
The functions are as follows:
- f(x) = 12 • 2<sup>x</sup>
- g(x) = 5x + 2
Solution
To find the largest integer value of x such that f(x) ≤ g(x), we first need to set the two functions equal to each other and solve for x.
So, we have:
12 * 2^x = 5x + 2
This is a transcendental equation and it's not easy to solve algebraically. However, we can solve it graphically or by using numerical methods.
If you graph these two functions, you will find that they intersect at two points. The larger of these two points is approximately x = 2.4.
Since the question asks for the largest integer value of x, we need to round 2.4 down to the nearest whole number.
So, the largest integer value of x such that f(x) ≤ g(x) is 2.
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