Question

Can someone help me solve this ?

Answer 1

$f(g(x))=x^2+4x+3$

Solution:

Given data:

$f(x)=x^{2}-1$

$g(x)=x+2$

To find f(g(x)):

Substitute g(x) into the function f(x).

$f(g(x))=f(x+2)$

           $f(g(x))=(x+2)^2-1$

Apply algebraic rule:

$(a+b)^{2}=a^{2}+2 a b+b^{2}$

$f(g(x))=x^2+2\times 2x+2^2-1$

$f(g(x))=x^2+4x+4-1$

$f(g(x))=x^2+4x+3$            

Therefore, $f(g(x))=x^2+4x+3$.