Answer:
[tex]fg(7)=143.95[/tex]
Step-by-step explanation:
We are given that
[tex]f(x) = (x -2)^2 -3[/tex] for x > −2
[tex]g(x) = 2x+6x^{-2}[/tex] for x > 2
We have to find fg(7)
[tex]fg(7)=f(g(7))[/tex]
[tex]=f(2(7)+6(7)^{-2})[/tex]
=[tex]f(14+\frac{6}{49})[/tex]
=[tex]f(\frac{692}{49})[/tex]
692/49>-2
fg(7)=[tex](\frac{692}{49}-2)^2-3[/tex]
=[tex]146.95-3[/tex]
Hence, [tex]fg(7)=143.95[/tex]
