Question

let f:IR-DIR be defined by f(x) = 31x), Prove that f(x)-31x1 is invertible. Compute the preimage f'((2,4]).

Answer 1

A be a function defined by 31211 FIRIR from To prove this is invertible it must shows that ( 7 f is bijective both and onto one f is 7 one but flow = 3 f(-1) = 31-1)= 3 f(1) = 3 (111) = 3 fl-1)= flis f is not one-one (bz, 18) > f is not envertible i.e.x70) if fix = 3x then fram must be envertible / for one-one f(x)= fles) 34, 5.342 n 2 X2 23 al - f is one-one conto ㅕ 게스로

for onto Let y = 31561 for x>0 y= 32 x= 7 3 IRIR f-llys- * f is onto y So, for xxo, few is einvertible and f-'( 20 = 2 3 4 f-1/2) = √ (2) = 4 (4) = f-'14 4 = 3 So, f\[24] = (13)
here f(x) is not invertible so ,if you break it just like x>0 or x<0 then it must be invertible and we can find its inverse as in solution ...please comments if you have any problems