Question

Suppose that ​f(x)=5x-2 and ​g(x)=-2x+5 .

​(a) Solve ​f(x)= 0.
​(b) Solve ​f(x)> 0.
​(c) Solve ​f(x)= ​g(x).
​(d) Solve ​f(x)<= ​g(x).
​(e) Graph y=​f(x) and y= ​g(x) and find the point that represents the solution to the equation ​f(x)= ​g(x).

Answer 1

The value of f(x) = 0 is x = 2/5

The value of f(x) > 0 is x > 2/5

The value of f(x) = g(x) is x = 1

The value of f(x) ≤ g(x) is x ≤ 1

The point that represents the solution of y = f(x) and y = g(x) is (1, 3)

How to evaluate the functions

From the question, we have the following parameters that can be used in our computation:

f(x) = 5x - 2

g(x) = -2x + 5

First, we have

f(x) = 0

This means that

5x - 2 = 0

5x = 2

So, we have

x = 2/5

This also means that

x > 2/5 for f(x) > 0

When f(x) = g(x), we have

5x - 2 = -2x + 5

Evaluate the like terms

7x = 7

So, we have

x = 1

This also means that

x ≤ 1 for f(x) ≤ g(x)

Graphing y = f(x) and y = g(x), we have the point that represents the solution to be (1, 3)