Question

If f(x) = x2 and g(x) = 4x + 3, find:
6) f(g(x))

Answer 1

Answer:

The composition of f and g is given by

$f(g(x))=4x(4x+6)+9$

Step-by-step explanation:

Given function f is defined by $f(x)=x^{2}$ and the

function g is defined by $g(x)=4x+3$

Now to find the composition of f and g:

ie.,to find f(g(x)):

we know that $(f \circ g)x=f(g(x))$

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

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

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

$f(g(x))=16x^{2}+24x+9$

$f(g(x))=4x(4x+6)+9$

Therefore  $f(g(x))=4x(4x+6)+9$

Therefore the  composition of f and g is  $f(g(x))=4x(4x+6)+9$