Question

evaluate the function for the given value of x.
$f(x) = 7x^4 - 10x^2 + 14x - 26$ ; $x = -7$
$f(-7) = \square$

Explanation:

Step1: Substitute \( x = -7 \) into the function.

We have \( f(x) = 7x^4 - 10x^2 + 14x - 26 \), so substitute \( x = -7 \):
\( f(-7)=7(-7)^4 - 10(-7)^2 + 14(-7) - 26 \)

Step2: Calculate each term.

• Calculate \( (-7)^4 \): \( (-7)^4 = (-7)\times(-7)\times(-7)\times(-7)=2401 \), so \( 7(-7)^4 = 7\times2401 = 16807 \)
• Calculate \( (-7)^2 \): \( (-7)^2 = 49 \), so \( -10(-7)^2 = -10\times49 = -490 \)
• Calculate \( 14(-7) \): \( 14\times(-7)= -98 \)

Step3: Combine all terms.

Now substitute these values back into the expression:
\( f(-7)=16807 - 490 - 98 - 26 \)
First, \( 16807 - 490 = 16317 \)
Then, \( 16317 - 98 = 16219 \)
Finally, \( 16219 - 26 = 16193 \)

Answer:

\( 16193 \)