Suppose `f(x)=(x+1)^2forxgeq-1.`If `g(x)`is the function whose graph is the reflection of the graph of `f(x)`with respect to the line `y=x ,`then `g(x)`equal.`a-sqrt(x)-1,xgeq0`(b) `1/((x+1)^2),x >-1``sqrt(x+1,)xgeq-1`(d) `sqrt(x)-1,xgeq0`A. `-sqrt(x)-1,x ge 0`B. `(1)/((x+1)^(2)), x gt -1`C. `sqrt(x+1), x ge -1`D. `sqrt(x) -1, x ge 0`

Suppose `f(x)=(x+1)^2forxgeq-1.`If `g(x)`is the function whose graph i

1.	Suppose `f(x)=(x+1)^2forxgeq-1.`If `g(x)`is the function whose graph is the reflection of the graph of `f(x)`with respect to the line `y=x ,`then `g(x)`equal.`a-sqrt(x)-1,xgeq0`(b) `1/((x+1)^2),x >-1``sqrt(x+1,)xgeq-1`(d) `sqrt(x)-1,xgeq0`A. `-sqrt(x)-1,x ge 0`B. `(1)/((x+1)^(2)), x gt -1`C. `sqrt(x+1), x ge -1`D. `sqrt(x) -1, x ge 0`
Answer» Correct Answer - D It is only to find the inverse. Let `y=f(x)=(x+1)^(2), " for " x ge -1` `pm sqrt(y)=x+1, x ge -1` `rArr sqrt(y)=x+1 rArr y ge 0, x+1 ge 0` `rArr x=sqrt(y) -1` `rArr f^(-1)(y)=sqrt(y)-1` `rArr f^(-1)(x)=sqrt(x)-1 rArr x ge 0`