QuestionAugust 24, 2025

Evaluate each function for the given value. 4 f(x)=-4x+7; f(1) 5.g(x)=2x^2+10x;g(-4) 9(-4)=2(-4)cdot 2+10(-4) 2(16)-40 6. f(1)+10 7. g(-9)+7 8. -2cdot g(4) 9. f(-4)-g(7)

Evaluate each function for the given value. 4 f(x)=-4x+7; f(1) 5.g(x)=2x^2+10x;g(-4) 9(-4)=2(-4)cdot 2+10(-4) 2(16)-40 6. f(1)+10 7. g(-9)+7 8. -2cdot g(4) 9. f(-4)-g(7)
Evaluate each function for the given value. 4 f(x)=-4x+7; f(1) 5.g(x)=2x^2+10x;g(-4) 9(-4)=2(-4)cdot 2+10(-4) 2(16)-40 6. f(1)+10 7. g(-9)+7 8. -2cdot g(4) 9. f(-4)-g(7)

Solution
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Answer

1. f(1) = 3 ### 2. g(-4) = -8 ### 3. f(1) + 10 = 13 ### 4. g(-9) + 7 = 79 ### 5. -2 \cdot g(4) = -144 ### 6. f(-4) - g(7) = -145 Explanation 1. Evaluate f(1) Substitute x = 1 into f(x) = -4x + 7: f(1) = -4(1) + 7 = -4 + 7 = 3. 2. Evaluate g(-4) Substitute x = -4 into g(x) = 2x^2 + 10x: g(-4) = 2(-4)^2 + 10(-4) = 2(16) - 40 = 32 - 40 = -8. 3. Calculate f(1) + 10 Use the result from Step1: f(1) = 3. So, f(1) + 10 = 3 + 10 = 13. 4. Calculate g(-9) + 7 Substitute x = -9 into g(x) = 2x^2 + 10x: g(-9) = 2(-9)^2 + 10(-9) = 2(81) - 90 = 162 - 90 = 72. Then, g(-9) + 7 = 72 + 7 = 79. 5. Calculate -2 \cdot g(4) Substitute x = 4 into g(x) = 2x^2 + 10x: g(4) = 2(4)^2 + 10(4) = 2(16) + 40 = 32 + 40 = 72. Then, -2 \cdot g(4) = -2 \cdot 72 = -144. 6. Calculate f(-4) - g(7) Substitute x = -4 into f(x) = -4x + 7: f(-4) = -4(-4) + 7 = 16 + 7 = 23. Substitute x = 7 into g(x) = 2x^2 + 10x: g(7) = 2(7)^2 + 10(7) = 2(49) + 70 = 98 + 70 = 168. Then, f(-4) - g(7) = 23 - 168 = -145.

Explanation

1. Evaluate $f(1)$<br /> Substitute $x = 1$ into $f(x) = -4x + 7$: $f(1) = -4(1) + 7 = -4 + 7 = 3$.<br /><br />2. Evaluate $g(-4)$<br /> Substitute $x = -4$ into $g(x) = 2x^2 + 10x$: $g(-4) = 2(-4)^2 + 10(-4) = 2(16) - 40 = 32 - 40 = -8$.<br /><br />3. Calculate $f(1) + 10$<br /> Use the result from Step1: $f(1) = 3$. So, $f(1) + 10 = 3 + 10 = 13$.<br /><br />4. Calculate $g(-9) + 7$<br /> Substitute $x = -9$ into $g(x) = 2x^2 + 10x$: $g(-9) = 2(-9)^2 + 10(-9) = 2(81) - 90 = 162 - 90 = 72$. Then, $g(-9) + 7 = 72 + 7 = 79$.<br /><br />5. Calculate $-2 \cdot g(4)$<br /> Substitute $x = 4$ into $g(x) = 2x^2 + 10x$: $g(4) = 2(4)^2 + 10(4) = 2(16) + 40 = 32 + 40 = 72$. Then, $-2 \cdot g(4) = -2 \cdot 72 = -144$.<br /><br />6. Calculate $f(-4) - g(7)$<br /> Substitute $x = -4$ into $f(x) = -4x + 7$: $f(-4) = -4(-4) + 7 = 16 + 7 = 23$. <br /> Substitute $x = 7$ into $g(x) = 2x^2 + 10x$: $g(7) = 2(7)^2 + 10(7) = 2(49) + 70 = 98 + 70 = 168$. <br /> Then, $f(-4) - g(7) = 23 - 168 = -145$.
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