Q Let f be real-valued invertible function such that
$f (\frac{2 x - 3}{x - 2}) = 5 x - 2, x \neq 2 . T h e n f i n d t h e v a l u e o f f^{- 1} (13) ?$

Question

Q Let f be real-valued invertible function such that
f 2 x - 3 x - 2 = 5 x - 2 ,   x ≠ 2   T h e n
  f i n d     t h e   v a l u e   o f
  f - 1 ( 13 ) ?

Aarushi Mishra · Accepted Answer

f2x-3x-2=5x-2, x≠2  _____________(1)Note: If we make 5x-2 into a single variable term say y then we can simply take inverse on both sides and thus evaluate f-113Let 5x-2=y5x=y+2x=y+25Put in equation 1f2y+25-3y+25-2=y, y+25≠2f2y+4-155y+2-105=y, y+2≠10f2y-11y-8=y  , y≠8Take inverse on both sidesf-1f2y-11y-8=f-1y  , y≠8Using f-1fx=x2y-11y-8=f-1y  , y≠8Now put y=13f-113=2×13-1113-8=155=3

Q Let f be real-valued invertible function such that f 2 x - 3 x - 2 = 5 x - 2 , x ≠ 2 . T h e n f i n d t h e v a l u e o f f - 1 ( 13 ) ?

Q Let f be real-valued invertible function such that
$f (\frac{2 x - 3}{x - 2}) = 5 x - 2, x \neq 2 . T h e n f i n d t h e v a l u e o f f^{- 1} (13) ?$