Question

If f(x) is 4x-3 what is (f^-1of) (10)

Answer 1

`f(x)=4x-3\ \ \ \ and\ \ \ D_f=R\\\\y=4x-3\ \ \ \Rightarrow\ \ \ y+3=4x\ /:4\ \ \ \Rightarrow\ \ \ (1)/(4)y+ (3)/(4)=x\\\\f^(-1)(x)= (1)/(4)x+ (3)/(4) \ \ \ \ and\ \ \ \ D_(f^(-1))=R\\\\ (f^(-1)\circ f) (10)=f^(-1)\bigg( f (10)\bigg)=\\=f^(-1)\bigg( 4\cdot10-3\bigg)=f^(-1)(37)=(1)/(4)\cdot37+ (3)/(4) =(37)/(4) +(3)/(4) = (40)/(4) =10`

Answer 2

`f(x)=4x-3\\ y=4x-3\\ 4x=y+3\\ x=(1)/(4)y+(3)/(4)\\ f^(-1)(x)=(1)/(4)x+(3)/(4)\\\\ f^(-1) \circ f=(1)/(4)(4x-3)+(3)/(4)\\ f^(-1) \circ f=(4x)/(4)-(3)/(4)+(3)/(4)\\ f^(-1) \circ f=x`