FIND THE VALUE OF X IN EVALUATING FUNCTION FOR THE GIVEN VALUE OF Y

Find the value(s) of x given that:

Problem 1 :

f(x) = 3x² - 2x + 5 and f(x) = 5

Solution:

f(x) = 3x² - 2x + 5

5 = 3x² - 2x + 5

3x² - 2x + 5 - 5 = 0

3x² - 2x = 0

x(3x - 2) = 0

x = 0 or 3x - 2 = 0

3x = 2

x = 2/3

So, the values of x are 0 and 2/3.

Problem 2 : 

f(x) = x² - x - 5 and f(x) = 1

Solution:

f(x) = x² - x - 5

1 = x² - x - 5

x² - x - 5 - 1 = 0

x² - x - 6 = 0

(x + 2) (x - 3) = 0

x + 2 = 0 or x - 3 = 0

x = -2 or x = 3

So, the values of x are -2 and 3.

Problem 3 :

f(x) = -2x² - 13x + 3 and f(x) = -4

Solution:

f(x) = -2x² - 13x + 3

-4 = -2x² - 13x + 3

-2x² - 13x + 3 + 4 = 0

-2x² - 13x + 7 = 0

-2x² + x - 14x + 7 = 0

x(-2x + 1) + 7 (-2x + 1) = 0

(x + 7) (-2x + 1) = 0

x + 7 = 0 or -2x + 1 = 0

x = -7 or -2x = -1

x = 1/2

So, the values of x are -7 and -1/2.

Problem 4 :

f(x) = 2x² - 12x + 1 and f(x) = -17

Solution:

f(x) = 2x² - 12x + 1

-17 = 2x² - 12x + 1

2x² - 12x + 1 + 17 = 0

2x² - 12x + 18 = 0

2(x² - 6x + 9) = 0

2(x - 3) (x - 3) = 0

x - 3 = 0

x = 3

So, the value of x is 3.