Question 155916
1){{{f(x)=x^2-4=0}}}
{{{x^2=4}}}
{{{x=2}}} and {{{x=-2}}}
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2){{{f(x)=x^2-4}}}
{{{g(x)=sqrt(2x+4)}}}
{{{f(g(x))=(sqrt(2x+4))^2-4}}}
{{{f(g(x))=(2x+4)-4}}}
{{{f(g(x))=2x}}}
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3){{{f(x)=x^2-4}}}
{{{g(x)=sqrt(2x+4)}}}
{{{g(f(x))=sqrt(2(x^2-4)+4)}}}
{{{g(f(x))=sqrt(2x^2-8+4)}}}
{{{g(f(x))=sqrt(2x^2-4)}}}
{{{g(f(0))=sqrt(2(0)^2-4)}}}
{{{g(f(0))=sqrt(-4)}}}
{{{g(f(0))=2*sqrt(-1)}}}
{{{g(f(0))=2i}}}
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1){{{f(x)=x^2-4}}}
{{{y=x^2-4}}} Use x,y nomenclature
{{{x=y^2-4}}} Interchange x and y
{{{y^2=x+4}}} Solve for y.
{{{y=0+-sqrt(x+4)}}}
{{{f^(-1)(x)=0+-sqrt(x+4)}}}