Question

Find the domain and range of the function f(x)=3x^2 - 5.also find f(-3)and the number which are associated with the number 43 in its range

Answer 1

Given : function is .., f(x) = 3x² - 5.

To find : the domain and range of the function f(x). also the value of f(-3) and the number which are associated with the number 43 in its range.

solution : we know, domain is the set of possible input values. i.e., the values of x for which function is defined.

while range is the set of possible output values.i.e., the values of y.

function, f(x) = 3x² - 5, is a polynomial function

so f(x) is defined for all real value of x.

therefore domain of the function, x ∈ R

range : let f(x) = y

y = 3x² - 5

⇒3x² - 5 - y = 0

⇒3x² - (5 + y) = 0

⇒x² = (5 + y)/3

⇒x = ±√[(5 + y)/3]

we know, square root is non negative function.

so, (5 + y)/3 ≥ 0

⇒5 + y ≥ 0

⇒y ≥ -5

therefore range of the function , y ∈ [-5, ∞)

now f(-3) = 3(-3)² - 5 = 3 × 9 - 5 = 27 - 5 = 22

the number which are associated with the number 43 in its range.

i.e., y = 43

⇒43 = 3x² - 5

⇒48 = 3x²

⇒x² = 16

⇒x = ±4

Therefore the numbers are ; 4 and -4