this function is what onto , many one , one one , into ?
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Verified answer
F( x ) = ln{ √(1+x⁴ ) - x²}first we check is this function one -one ??
we know , that any function y= f(x) will be one-one only when , dy/dx is strictly increasing or strictly decreasing .
now, differentiate f(x) wrt x
dy/dx = 1/{√(1+ x⁴) - x²} × { 4x³/2√(1+x⁴) -2x }
= 1/{ √( 1+x⁴)-x²} ×2{ x³- x√(1+x⁴)}/√(1+x⁴)
= -2×x/√(1+x⁴ )
= -2x/√(1+x⁴)
we know, exponential function always positive so, √(1+x⁴)> 0
but - ∞ < x < ∞
so, dy/dx is positive as well as negative e.g dy/dx >0 or < 0
so , function is many- one function .