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Determine f –1(x) if f of x is equal to the quantity x plus 3 end quantity over the quantity x minus 4 end quantity where x ­ 4.
f inverse of x is equal to the quantity x minus 1 end quantity over the quantity 4 times x plus 3 end quantity
f inverse of x is equal to the quantity 4 times x plus 3 end quantity over the quantity x minus 1 end quantity
f inverse of x is equal to the quantity x minus 4 end quantity over the quantity x plus 3 end quantity
f inverse of x is equal to the quantity x minus 3 end quantity over the quantity x plus 4 end quantity

Determine f 1x if f of x is equal to the quantity x plus 3 end quantity over the quantity x minus 4 end quantity where x 4 f inverse of x is equal to the quanti class=

Respuesta :

mhanifa

Answer:

  • Option B

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)

Correct choice is B
  • y=x+3/(x-4)

Interchange x and y and solve

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

That's the inverse

Option B

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