Given:
The functions are:
[tex]f(x)=x+7[/tex]
[tex]g(x)=x^2-3[/tex]
To find:
The values f(g(4)), g(f(5)) and f(f(1)).
Solution:
We have,
[tex]f(x)=x+7[/tex]
[tex]g(x)=x^2-3[/tex]
(i) We need to find the value of f(g(4)).
[tex]f(g(4))=f((4)^2-3)[/tex]
[tex]f(g(4))=f(16-3)[/tex]
[tex]f(g(4))=f(13)[/tex]
[tex]f(g(4))=13+7[/tex]
[tex]f(g(4))=20[/tex]
Therefore, the value of f(g(4)) is 20.
(ii) We need to find the value of g(f(5)).
[tex]g(f(5))=g(5+7)[/tex]
[tex]g(f(5))=g(12)[/tex]
[tex]g(f(5))=(12)^2-3[/tex]
[tex]g(f(5))=144-3[/tex]
[tex]g(f(5))=141[/tex]
Therefore, the value of g(f(5)) is 141.
(iii) We need to find the value of f(f(1)).
[tex]f(f(1))=f(1+7)[/tex]
[tex]f(f(1))=f(8)[/tex]
[tex]f(f(1))=8+7[/tex]
[tex]f(f(1))=15[/tex]
Therefore, the value of f(f(1)) is 15.
