Chapter 4, Problem 14RE

To determine

To find: The value of $f\left(x\right)=12x^6-8x^4+1$ at $x=4$ .

Answer to Problem 14RE

The value of $f\left(x\right)=12x^6-8x^4+1=47105$.

Explanation of Solution

Given information: $f\left(x\right)=12x^6-8x^4+1$

Solution:

Let’s $f\left(x\right)=y=12x^6-8x^4+1---\left(i\right)$

We put the value $x=4$ in the given equation $-\left(i\right)$

  $\begin{array}{l}f\left(4\right)=12\times 4^6-8\times 4^4+1\\ =\left(12\times 4096\right)-\left(8\times 256\right)+1\\ =49152-2048+1\\ =47105\end{array}$

Hence, the value of $f\left(x\right)=12x^6-8x^4+1=47105$.