If #f(x) = sqrt(1+x)# and #g(x) = (3x^2)/(x^2+1)#, what is #g[f(x)]#?

Question

What is the range of #g#?

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Answer 1 · 2016-09-01T11:12:08

Answer is:

#g[f(x)]=3(1+x)/(2+x)#

#f(x)=sqrt(1+x)#

#g(x)=(3x^2)/(x^2+1)#

For #g[f(x)]# substitute #f(x)# instead of #x# in the #g(x)# function:

#g[f(x)]=(3sqrt(1+x)^2)/(sqrt(1+x)^2+1)#

#g[f(x)]=(3(1+x))/((1+x)+1)#

#g[f(x)]=3(1+x)/(1+x+1)#

#g[f(x)]=3(1+x)/(2+x)#