Helpp pls The function f is defined by the equation
f(x) = (x - b)^2, where b is a constant. If
f(5) = f(9), what is the value of f(1) ?
A) 25
B) 36
C) 45
D) 49

B

Step-by-step explanation:

Substitute x = 5 and x = 9 into f(x) and equate

f(5) = (5 - b)² = 25 - 10b + b²

f(9) = (9 - b)² = 81 - 18b + b²

Then equating the 2 gives

b² - 10b + 25 = b² - 18b + 81 ( subtract b² - 18b from both sides )

8b + 25 = 81 ( subtract 25 from both sides )

8b = 56 ( divide both sides by 8 )

b = 7

Then

f(x) = (x - 7)² and

f(1) = (1 - 7)² = (- 6)² = 36 → B

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true

you just switch the numbers basically so it would be 3/17