Answer:the solutions to f(x) = 7 are x = 7 and x = -1.
Step-by-step explanation:a. To evaluate f(2), we substitute x = 2 into the function f(x) = x² - 6x:
f(2) = (2)² - 6(2)
= 4 - 12
= -8
Therefore, f(2) = -8.
b. To solve f(x) = 7, we set the equation equal to 7 and solve for x:
x² - 6x = 7
To solve this quadratic equation, we bring all terms to one side:
x² - 6x - 7 = 0
Now, we can factor or use the quadratic formula to solve for x. Factoring this equation might not be possible, so we'll use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
In our case, a = 1, b = -6, and c = -7. Substituting these values into the formula, we get:
x = (-(-6) ± √((-6)² - 4(1)(-7))) / (2(1))
x = (6 ± √(36 + 28)) / 2
x = (6 ± √64) / 2
x = (6 ± 8) / 2
Simplifying further, we have two possible solutions:
x₁ = (6 + 8) / 2 = 14 / 2 = 7
x₂ = (6 - 8) / 2 = -2 / 2 = -1