Find the inverse
Algebra

Step-by-step explanation:

a) k(x) = (x - 2)² - 4 → x = (y - 2)² - 4 → (y - 2)² = x + 4 → y - 2 = ±√( x + 4) → y = 2 ±√( x + 4) → k-¹(x) = 2 ±√( x + 4)

b) f(x) = ½(x + 2)² - 3 → x = ½(y + 2)² - 3 → ½(y + 2)² = x + 3 → (y + 2)² = 2x + 6 → y + 2 = ±√(2x + 6) → y = -2 ±√(2x + 6) → f-¹(x) = - 2 ±√(2x + 6)

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.