Answer :

To find [tex]\( f(-5) \)[/tex] for the function [tex]\( f(x) = 5x^3 - 7x + 19 \)[/tex], we need to substitute [tex]\(-5\)[/tex] for [tex]\( x \)[/tex] in the function.

Here's a step-by-step guide:

1. Identify the Function: The function given is [tex]\( f(x) = 5x^3 - 7x + 19 \)[/tex].

2. Substitute [tex]\( x = -5 \)[/tex] into the Function:
- Replace every occurrence of [tex]\( x \)[/tex] in the equation with [tex]\(-5\)[/tex].

[tex]\[
f(-5) = 5(-5)^3 - 7(-5) + 19
\][/tex]

3. Calculate Each Term:
- First, calculate [tex]\((-5)^3\)[/tex]:
[tex]\[
(-5)^3 = -125
\][/tex]
- Multiply by 5:
[tex]\[
5 \times (-125) = -625
\][/tex]

- Next, calculate the second term [tex]\(-7(-5)\)[/tex]:
[tex]\[
-7 \times (-5) = 35
\][/tex]

- The constant term is 19.

4. Combine All the Terms:
- Add the results from above:
[tex]\[
f(-5) = -625 + 35 + 19
\][/tex]

5. Calculate the Sum:
- Combine the numbers:
[tex]\[
-625 + 35 = -590
\][/tex]
- Add 19:
[tex]\[
-590 + 19 = -571
\][/tex]

Therefore, the value of [tex]\( f(-5) \)[/tex] is [tex]\(-571\)[/tex].

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