f f(x)=3x+2 and g(x)=x2−x, find the value.

Question

f f(x)=3x+2

and g(x)=x2−x,

find the value.

Answer 1

I will assume that the purpose of this problem is to find the value of x if f(x) = g(x), although that part of the question seems to be missing. So let's take the problem as follows:

If f(x) = 3x + 2 and g(x) = x² - x, find the value that makes f(x) = g(x).

Setting the two functions equal to each other we get:

3x + 2 = x² - x

We then rearrange the quadratic equation so that it is set equal to 0.

3x + 2 -3x = x² - x - 3x

2 = x² - 4x

2 - 2 = x² - 4x - 2

0 = x² - 4x - 2

From here, the equation is best solved using the quadratic formula.

x = [-b ± √(b² - 4ac)] ⁄ (2a)

Substituting in the values a = 1, b = -4, and c = -2 we get:

x = [-(-4) ± √((-4)² - 4(1)(-2))] ⁄ 2(1)

x = [4 ± √(16 + 8)] ⁄ 2

x = (4 ± √24) ⁄ 2

Simplifying but keeping in exact form gives us:

x = (4 ± 2√6) ⁄ 2

This means our quadratic provided two possible solutions, which also can be interpreted as the graph having two x-intercepts (zeros).