Question

4. I need help with question in the attached picture!

Answer 1

Answer:

Option D is correct.

Step-by-step explanation:

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

We know that f(a) =b ⇔ f^-1 (b) =a

Using this,

We are given $f^{-1}(3)=x => f(x)=3$

and $f(x)= \frac{2x+2}{x-4}$

putting value of f(x)

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

Option D is correct.

Answer 2

ANSWER

D. 13

EXPLANATION

We have

$f(x) = \frac{2x + 1}{x - 4}$

To find

${f}^{ - 1} (3)$

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

$\frac{2x + 1}{x - 4} = 3$

We cross multiply,

$2x + 1 = 3(x - 4)$

Expand:

$2x + 1 = 3x - 12$

Combine like terms,

$3x - 2x = 12 + 1$

$x = 13$

$\therefore{f}^{ - 1} (3)= 13$