Question

a) Rewrite the following in nested form and hence evaluate at the given value of x:
(i) f(x) = 4x4 + 3x2+2x - 4 [x=2]
(ii) f(x) = 2x4 + x3+3x2 + 5x - 6 [x=3]

Answer 1

(i) $f(x)=4x^4+3x^2+2x-4$

Write $f$ in the nested form:

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

For $x=2$ calculate the value of the function $f$ :

$f(2)=(((4\cdot 2)2+3)2+2)2-4=((8\cdot 2+3)2+2)2-4=(19\cdot 2+2)2-4=40\cdot 2-4=76$

(ii) $f(x)=2x^4+x^3+3x^2+5x-6$

Write $f$ in the nested form:

$f(x)=2x^4+x^3+3x^2+5x-6=(2x^3+x^2+3x+5)x-6=((2x^2+x+3)x+5)x-6=(((2x+1)x+3)x+5)x-6$

For $x=3$ calculate the value of the function $f$ :

$f(3)=(((2\cdot 3+1)3+3)3+5)3-6=((7\cdot 3+3)3+5)3-6=(24\cdot 3+5)3-6=77\cdot 3-6=225$