Question

Does anyone know this

Answer 1

Given:

The functions are:

$f(x)=x+7$

$g(x)=x^2-3$

To find:

The values f(g(4)), g(f(5)) and f(f(1)).

Solution:

We have,

$f(x)=x+7$

$g(x)=x^2-3$

(i) We need to find the value of f(g(4)).

$f(g(4))=f((4)^2-3)$

$f(g(4))=f(16-3)$

$f(g(4))=f(13)$

$f(g(4))=13+7$

$f(g(4))=20$

Therefore, the value of f(g(4)) is 20.

(ii) We need to find the value of g(f(5)).

$g(f(5))=g(5+7)$

$g(f(5))=g(12)$

$g(f(5))=(12)^2-3$

$g(f(5))=144-3$

$g(f(5))=141$

Therefore, the value of g(f(5)) is 141.

(iii) We need to find the value of f(f(1)).

$f(f(1))=f(1+7)$

$f(f(1))=f(8)$

$f(f(1))=8+7$

$f(f(1))=15$

Therefore, the value of f(f(1)) is 15.