Question

If f(x)=5x-12, find a value for $x$ so that f^{-1}(x)=f(x+1).

Answer 1

Answer:

Step-by-step explanation:

let f(x)=y

y=5x-12

flip x and y

x=5y-12

5y=x+12

$y=\frac{x+12}{5} \\or \\f^{-1}(x)=\frac{x+12}{5} \\f(x+1)=5(x+1)-12=5x-7\\\frac{x+12}{5} =5x-7\\x+12=25x-35\\25~x-x=12+35\\24 x=47\\x=\frac{47}{24}$

Answer 2

Answer:

$\boxed{\sf \ \ \ x=\dfrac{47}{24} \ \ \ }$

Step-by-step explanation:

Hello,

f(x)=5x-12

we need to find x so that

$f^{-1}(x)=f(x+1)$

so first of all we can write

$x = (fof^{-1})(x)=f(f^{-1}(x))=5f^{-1}(x)-12\\\\5f^{-1}(x)=x+12\\\\f^{-1}(x)=\dfrac{x+12}{5}$

and f(x+1) = 5(x+1) - 12 = 5x + 5 -12 = 5x - 7

then solving

$f^{-1}(x)=f(x+1)$

is equivalent to

$\dfrac{x+12}{5}=5x-7 \ multiply \ by \ 5 \\\\ x+12 = 5(5x-7)=25x-35\\ 25x-x=12+35\\\\24x=47\\\\x=\dfrac{47}{24}$

Hope this helps