For each of the following functions f : R?R, determine whether f is invertible,

Question

For each of the following functions f : R?R, determine whether f is invertible, and, if so, determine f ?1. a) f = {(x, y)|2x + 3y = 7} b) f={(x,y)|ax+by=c,b?0} c) f = {(x, y)|y = x3} d) f = {(x, y)|y = x4 + x

Explanation / Answer

a) 2x+3y=7 => 2x= 7-3y => y= (7-3y)/2 f is invertible and finverse(x)= (7-3x)/2 b) ax+by=c, b>0 => ax=c-by => y=1/a*(c-by) if a is not equal to 0, f is invertible and finverse(x)=1/a*(c-by) c) y=x^3 => x=cuberoot(y) hence f is invertible and finverse(x)=cuberoot(x) d) x^4+x=y.. f is surjective as it attains all values in R... suppose f(0)= f(-1)=0 hence f is not injective.. hence f is not invertible.. PLEASE RATE MY ANSWER FIRST IF YOU LIKE IT :)

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