Answer:
function’s input value is x = 2, 7/2.
Step-by-step explanation:
Given : f(x) = 2x² + 3x + 5 when evaluated, gives a value of 19.
To find : What is the function’s input value.
Solution : We have given that f(x) = 2x² + 3x + 5
2x² + 3x + 5 = 19
On subtracting on side by 19
2x² + 3x + 5 -19 = 0
2x² + 3x - 14 = 0
On factoring
2x² - 4x + 7x -14 = 0
Taking common 2x from first two terms and 7 from last two terms
2x( x - 2 ) + 7 ( x - 2 ) = 0
On grouping
( 2x + 7) ( x -2) = 0
x - 2 = 0
x = 2 ,
2x + 7 =0
x = -7/2 .
Let check for both values 2(2)² + 3(2) + 5 = 8 +6 +5 = 19.
2(7/2)² + 3(-7/2) + 5 = 24.5 - 10.5 + 5 = 19
Therefore, function’s input value is x = 2, 7/2.