Determine how to construct the functions using only elementa

Determine how to construct the functions using only elementary functions, and the operations of +, , ×, ÷, and . f(x) = x^ 2 tan ( e^ xx /1 + ln x )

Solution

f(x) = x^ 2 tan ( e^ xx /1 + ln x )

1) take elementary functions y1 = x^2 and y2 = tanx

2) Also take elementary functions y3,y4 , y5 : sqrtx and e^x and ln(x)

3) Now ,vertical shift ln(x) by 1 unit y5: 1+lnx

multiply two functions e^x and sqrtx : y3*y4= sqrtx e^x

4) divide the last two function obtained : y3*y4/y5 =sqrtx*e^x/( 1+ lnx)

Let this be y\' =sqrtx*e^x/( 1+ lnx)

5)Now take the basic function y2 = tanx

find ( y2 o y\') = tan[sqrtxe^x/( 1+ lnx)]

6) Last multiply the above function with y1 = x^2

f(x) =( y2 o y\') *y1 = x^2 tan[sqrtxe^x/( 1+ lnx)]