Suppose that `g(x)=1+sqrt(x) " and " f(g(x))=3+2sqrt(x)+x.` Then find – InterviewSolution

1.	Suppose that `g(x)=1+sqrt(x) " and " f(g(x))=3+2sqrt(x)+x.` Then find the function `f(x)`.
Answer» `g(x)=1+sqrt(x) " and " f(g(x))=3+2sqrt(x)+x " " `(1) ` :. f(1+sqrt(x))=3+2sqrt(x)+x` Put `1+sqrt(x)=y " or " x=(x-y)^(2).` Then, `f(y)=3+2(y-1)+(y-1)^(2)=2+y^(2).` ` :. f(x)=2+x^(2)`

Discussion

No Comment Found

Related InterviewSolutions

One cubic meter piece of copper is melted and recast into a bar 36 meters long with a square cross-sectional area. An exact cube is cut off from this bar. The cost of this cube, if 1 m3 of copper costs Rs.216 will be :
If `(x-2,y+5)=(2,(1)/(3))` are two equal ordered paris, then `x=4, y=(-14)/(3)`
If `f(x)=(4x+3)/(6x-4), x !=2/3,`show that `fof(x)=x`for all `x!=2/3dot`What is the inverse of `f?`
The number of roots of `x^2-2=[sinx],w h e r e[dot]`stands for the greatest integer function is0 (b)1 (c) 2(d) 3.
Domain of the function, `f(x)=[log_10 ((5x-x^2)/4)]^(1/2)` isA. `-oo lt x lt oo`B. `1 le x le 4 `C. `4 le x le 16`D. ` -1 le x le 1`
The period of `f(x)=[x]+[2x]+[3x]+[4x]+[n x]-(n(n+1))/2x ,`where `n in N ,`is (where `[dot]`represents greatest integer function).`n`(b) 1(c) `1/n`(d) none of theseA. nB. 1C. `(1)/(n)`D. none of these
The derivative of `log_10 x` is ?
Find the value of x `tan^-1 ((x-1)/(x+1)) + tan^-1 ((2x-1)/(2x+1)) = tan^-1 (23/36)`
Let [ ] represents the greatest integer function and `[ x^3 + x^2 + 1 + x] = [ x^3 + x^2 + 1] + x`. The number of solution of the equation log|[x]| = 2 - |[x ]|
a bag contains lemon flavored candies only. Malini takes out one candy without looking into the bag . What is the probability that she takes out(i) an orange flavored candy ? (ii) an lemon flavored candy ?