contestada

Determine f –1(x) if f of x is equal to the quantity x plus 2 end quantity over the quantity x minus 3 end quantity where x ≠ 3.


f inverse of x is equal to the quantity x minus 3 end quantity over the quantity x plus 2 end quantity
b
f inverse of x is equal to the quantity x minus 2 end quantity over the quantity x plus 3 end quantity
c
f inverse of x is equal to the quantity x minus 1 end quantity over the quantity 3 times x plus 2 end quantity
d
f inverse of x is equal to the quantity 3 times x plus 2 end quantity over the quantity x minus 1 end quantity

Respuesta :

lukelaws

Answer: f inverse of x is equal to the quantity 3 times x plus 2 end quantity over the quantity x minus 1 end quantity

f⁻¹(x) = (4x + 3) / (x - 1) is the answer

Step-by-step explanation:

Given function:

f(x) = (x + 3)/(x - 4)

Find its inverse, take f(x) as y and swap x with y

x = (y + 3)/(y - 4)

x = (y - 4 + 7) / (y - 4)

x = 1 + 7/(y - 4)

x - 1 = 7 / (y - 4)

y - 4 = 7 / (x - 1)

y = 4 + 7 / (x - 1)

y = (4x - 4 + 7)/ (x - 1)

y = (4x + 3) / (x - 1)

Replace y with f⁻¹(x):

f⁻¹(x) = (4x + 3) / (x - 1)