Question

If f(x)=9-4x^2 Finda) f(-2) b) f(-3) f(3) c) x such that f(x) = 0​

Answer 1

Answer:

see explanation

Step-by-step explanation:

(a)

To evaluate f(- 2) substitute x = - 2 into f(x) , that is

f(- 2) = 9 - 4(- 2)² = 9 - 4(4) = 9 - 16 = - 7

(b)

Similarly substitute x = - 3 and x = 3 into f(x)

f(- 3) = 9 - 4(- 3)² = 9 - 4(9) = 9 - 36 = - 27

f(3) = 9 - 4(3)² = 9 - 4(9) = 9 - 36 = - 27

(c)

let f(x) = 0 , then

9 - 4x² = 0 ( add 4x² to both sides )

9 = 4x² ( divide both sides by 4 )

$\frac{9}{4}$ = x² ( take the square root of both sides )

± $\sqrt{\frac{9}{4} }$ = x

± $\frac{\sqrt{9} }{\sqrt{4} }$ = x

± $\frac{3}{2}$ = x

That is x = - $\frac{3}{2}$ or x = $\frac{3}{2}$