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# Need help!

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

Jul 23, 2017

#1
+1

f(x)  =  5x - 12

Let's say...

y  =  5x - 12

Now solve this equation for  x  .

y + 12  =  5x

(y + 12) / 5  =  x

To get the inverse function, swap  x  and  y  . Instead of  " y "  I put   " f-1(x) "

f-1(x)  =  (x + 12) / 5

And we want to find what  x  value makes...

f-1(x)  =  f(x + 1)

That is...

(x + 12) / 5  =  5(x + 1) - 12

Multiply both sides by  5  .

x + 12  =  25(x + 1) - 60

x + 12  =  25x + 25 - 60

Subtract  25x  from both sides and subtract  12  from both sides.

x - 25x  =  -12 + 25 - 60

-24x  =  -47

x  =  47/24

Jul 23, 2017

#1
+1

f(x)  =  5x - 12

Let's say...

y  =  5x - 12

Now solve this equation for  x  .

y + 12  =  5x

(y + 12) / 5  =  x

To get the inverse function, swap  x  and  y  . Instead of  " y "  I put   " f-1(x) "

f-1(x)  =  (x + 12) / 5

And we want to find what  x  value makes...

f-1(x)  =  f(x + 1)

That is...

(x + 12) / 5  =  5(x + 1) - 12

Multiply both sides by  5  .

x + 12  =  25(x + 1) - 60

x + 12  =  25x + 25 - 60

Subtract  25x  from both sides and subtract  12  from both sides.

x - 25x  =  -12 + 25 - 60

-24x  =  -47

x  =  47/24

hectictar Jul 23, 2017