Question

Let f(x)= 3+or+8, then value of x for which
1'(x)=0 is​

Answer 1

Answer:

•f(x) =x2is not 1-to-1.•f(x) =x3is 1-to-1.•f(x) =1xis 1-to-1.•f(x) =xn−x,n>0, is not 1-to-1.Proof.•f(x1) =f(x2)⇒3x1−5 = 3x2−5⇒x1=x2.  Ingeneral,f(x) =ax−b,a6= 0, is 1-to-1.•f(1) = (1)2= 1 = (−1)2=f(−1). In general,f(x) =xn,neven, is not1-to-1.•f(x1) =f(x2)⇒x31=x32⇒x1=x2. In general,f(x) =xn,nodd, is 1-to-1.•f(x1) =f(x2)⇒1x1=1x2⇒x1=x2. In general,f(x) =x−n,nodd, is 1-to-1.•f(0) = 0n−0 = 0 = (1)n−1 =f(1). In general, 1-to-1 offandgdoesnot always imply 1-to-1 off+g