Let `f` be a function `N → N` be defined by `f(x)=x+3`, Find the pre-Image of `20,25,50`.

Answer

`ararrq,brarrp,crarrs,drarrr`

Explanation

(a) `f(x)=sinx-x^(2)+1`
f(x)=cos x-2x

or `f(x)lt0for xgtx_(0)`
and `f(X)gt0 for x lt x_(0)`
Hecne `x=x_(0)`is the point of maxima
(b) `f(X)=xlog_(e)x0-x+e^(-x)`
`f(X)=log_(e)x+1-1-e^(x)=log_(e)x-e^(-x)`

From the graph for `xltx_(0)e^(-x)gtlog_(e)x or f(X)`
for `xgtx_(0)lt log_(e)x or f(x)gt0`
Hence x`x=x_(0)` is point of minima
(c ) `f(x)=-x^(3)+2x^(2)-3x+1`
`f(X)=-3x^(2)+4x-3`
Now `D=16-4(-3)(-3)=-20lt0`
Hence `f(x)gt0` for all rel x
Thus f(x) is always decerasing
(d) `f(x)=cos pix+10x3x^(2)+x^(3)`
or `f(X)=-pisin pix+10+6x+3x^(2)`
`=3(x^(2)+2x+10//3)-pisin pix`
`=3((x+1)^(2)+7//3)-pisinpix`
Now minimum value of `3(x+1)^(2)+7//3` is 7 but
Maximum value of `p isin pi x is pi`
Hence `f(x)gt0` for all real x
Hecne f(x) is always incresing