Question 933421
Let {{{f(x)= x^2+2}}} and {{{g(x)=x+1}}}

a){{{f(2)}}}=

{{{f(2)= 2^2+2}}}
{{{f(2)= 4+2}}}
{{{f(2)= 6}}}

b){{{g(x)=7}}}
{{{7=x+1}}}
{{{7-1=x}}}
{{{6=x}}}


c){{{f(g(3))}}}=
first find {{{g(3)}}}
{{{g(3)=3+1}}}
{{{g(3)=4}}}...plug it in for {{{x}}} in {{{f(x)}}}

{{{f(4)= 4^2+2}}}
{{{f(4)=16+2}}}
{{{f(4)=18}}}

or
{{{f(g(3))=(x+1)^2+2}}}

{{{f(g(3))=(3+1)^2+2}}}

{{{f(g(3))=4^2+2}}}

{{{f(g(3))=16+2}}}

{{{f(g(3))=18}}}


d){{{g(f(x))}}}=

{{{g(f(x))=x^2+2+1}}}

{{{g(f(x))=x^2+3}}}


e) {{{f^-1(x)}}}=

{{{f(x)= x^2+2}}}....since {{{f(x)= y}}} we have

{{{y= x^2+2}}} ...swap {{{x}}} and {{{y}}}

{{{x= y^2+2}}}...solve for {{{y}}}

{{{x-2= y^2}}}

{{{sqrt(x-2)= y}}}

so,{{{f^-1(x)}}}=± {{{sqrt(x-2))}}}