Huang Wang
01/17/2024 · Elementary School
\( g(x)=2 x^{2}+1 \) \( h(x)=x-3 \) Find \( (g-h)(-5) \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To find \( (g - h)(-5) \), we first need to determine the expressions for \( g(x) \) and \( h(x) \).
Given:
\[
g(x) = 2x^2 + 1
\]
\[
h(x) = x - 3
\]
Now, we can find \( (g - h)(x) \):
\[
(g - h)(x) = g(x) - h(x) = (2x^2 + 1) - (x - 3)
\]
Simplifying this expression:
\[
(g - h)(x) = 2x^2 + 1 - x + 3 = 2x^2 - x + 4
\]
Next, we need to evaluate \( (g - h)(-5) \):
\[
(g - h)(-5) = 2(-5)^2 - (-5) + 4
\]
Calculating \( (-5)^2 \):
\[
(-5)^2 = 25
\]
Now substituting this back into the expression:
\[
(g - h)(-5) = 2(25) - (-5) + 4
\]
\[
= 50 + 5 + 4
\]
\[
= 50 + 5 + 4 = 59
\]
Thus, the final result is:
\[
\boxed{59}
\]
Quick Answer
\( (g - h)(-5) = 59 \)
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