If `f : R to R` is defined as:
`f(x)={{:(2x+5","x gt 9),(x^(2)-1","-9 lt x lt 9),(x-4"," lt -9):}`
then evaluate (i) `f(2), (ii) f(10),(iii) f(-12) and (iv) f[f(3)]`.

Answer

N/a

Explanation

(i) For `f(2)`
`-9 lt 2 lt 9`
`therefore` From `f(x)=x^(2) -1`
`f(2) =2^(2)-1 =4 -1 =3`
(ii) For `f(10)`
`10 gt 9`
`therefore ` from `f(x) =2x+5`
`f(10)=2xx10+5=25`
(iii) For `f(-12)`
`-12 lt -9`
`therefore f(x) =x-4`
`f(-12)=-12-4=-16`
(iv) For f `[f(3)]`
`-9 lt 3 lt 9`
`therefore ` From `f(x)=x^(2)-1`
`f(3)=3^(2)-1=8`
Again `-9 lt 8 lt 9`
`therefore ` from `f(x)=x^(2)-1`
`f[f(3)]=f(8)-8^(2)-1`
=63