Question

Question of function. If f(x+1) = x²-1 and g(x+2) = 5x+7.. and if fog (x) =X . Find the value of X.

Answer 1

Answer:

Explanation:

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

We will substitute x-1 in place of x

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

Now,

$g(x+2)=5x+7$

We will substitute x-2 in place of x

$g(x-2+2)=5(x-2)+7\\g(x)=5x-3$

fog(x) = f(g(x))

$f(g(x))=g(x)(g(x)-2)=(5x-3)(5x-3-2)=(5x-3)(5x-5)=25x^2-40x+15$

fog(x) = (5x-3)(5x-5)

Hope it helps :-)