Respuesta :

kudzordzifrancis

ANSWER

D. 13

EXPLANATION

We have

[tex]f(x) = \frac{2x + 1}{x - 4} [/tex]

To find

[tex] {f}^{ - 1} (3)[/tex]

means we want to find an x-value whose image is 3.

[tex]\frac{2x + 1}{x - 4} = 3[/tex]

We cross multiply,

[tex]2x + 1 = 3(x - 4)[/tex]

Expand:

[tex]2x + 1 = 3x - 12[/tex]

Combine like terms,

[tex]3x - 2x = 12 + 1[/tex]

[tex]x = 13[/tex]

[tex] \therefore{f}^{ - 1} (3)= 13[/tex]

absor201

Answer:

Option D is correct.

Step-by-step explanation:

[tex]f(x)= \frac{2x+1}{x-4} \,\,find \,\,value\,\,of\,\, f^{-1}(3)[/tex]

We know that f(a) =b ⇔ f^-1 (b) =a

Using this,

We are given [tex]f^{-1}(3)=x => f(x)=3[/tex]

and [tex]f(x)= \frac{2x+2}{x-4}[/tex]

putting value of f(x)

[tex]3= \frac{2x+1}{x-4}\\3(x-4) = 2x+1\\3x-12 = 2x+1\\Adding\,\,like\,\,terms\,\,\\3x-2x = 12+1\\x=13\\So, f^{-1}(3) = 13[/tex]

Option D is correct.

Otras preguntas

Q&A Education