Question

Question 23 . > 1 if x = 3 and f(x) = x2 – 3 and g(x) = then g(f(x))

Answer 1

g(f(0)
and  
f(g(2)
are known as composition function. To solve for
g(f(0)
, first write the given value of $\large f(x)$   , then express  $\large f(x)$ as x is expressed in the function
(2) 6
.

Similarly we can do the same for solving .

f(g(2)

From algebra, $\large (a-b)^2=a^2-2(a)b)+b^2$

  $\large f(x)=x^2-3$ and  $\large g(x)=\frac{1}{x}$

then $\large g(f(x))=$   $\large g(x^2-3)=$  $\large \frac{1}{x^2-3}$  

So,   $\large g(f(x))=\frac{1}{x^2-3}$

When,  x=3, then ,

  $\large g(f(3)) = \frac{1}{3^2-3}=\frac{1}{9-3}=\frac{1}{6}$

Now, $\large f(x)=x^2+3$ and   $\large g(x)=x-2$

  $\large f(g(x))=f(x-2) = (x-2)^2+3$

So,  $\large f(g(x))=(x^2-2(x)(2)+2^2)+3$

  $\large =(x^2-4x+4)+3$

  $\large =x^2-4x+7$

  $\large f(g(x))=x^2-4x+7$

When x=3,

$\large f(g(3))=3^2-4(3)+7$

$\large =9-12+7$

$\large =4$