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lions [1.4K]
2 years ago
14

Evaluate (f-g)(3t) for f(x)=x²+1 and g(x)=x-4

Mathematics
2 answers:
zysi [14]2 years ago
6 0
(f-g)(3t) \\  \\ f(x)-g(x) \\  \\ f(3t)-g(3t) \\  \\ ((3t)^2+1)-((3t)-4) \\  \\ 9t^2+1-3t+4 \\  \\ 9t^2-3t+5
Pavlova-9 [17]2 years ago
5 0
F(x)=x²+1

g(x)=x-4

------------

f(x)-g(x)

=x²+1-(x-4)

=x²+1-x+4

=x²-x+5

------------

Therefore:

(f-g)(3t)

=(3t)²-3t+5

=3²t²-3t+5

=9t²-3t+5
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Answer:

527

Step-by-step explanation:

237.15/0.45 = 527

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Answer:

5/8

Step-by-step explanation:

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F(x) = 3x + x3
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Answer:

Please check the explanation.

Step-by-step explanation:

Given

f(x) = 3x + x³

Taking differentiate

\frac{d}{dx}\left(3x+x^3\right)

\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'

=\frac{d}{dx}\left(3x\right)+\frac{d}{dx}\left(x^3\right)

solving

\frac{d}{dx}\left(3x\right)

\mathrm{Take\:the\:constant\:out}:\quad \left(a\cdot f\right)'=a\cdot f\:'

=3\frac{d}{dx}\left(x\right)

\mathrm{Apply\:the\:common\:derivative}:\quad \frac{d}{dx}\left(x\right)=1

=3\cdot \:1

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now solving

\frac{d}{dx}\left(x^3\right)

\mathrm{Apply\:the\:Power\:Rule}:\quad \frac{d}{dx}\left(x^a\right)=a\cdot x^{a-1}

=3x^{3-1}

=3x^2

Thus, the expression becomes

\frac{d}{dx}\left(3x+x^3\right)=\frac{d}{dx}\left(3x\right)+\frac{d}{dx}\left(x^3\right)

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Thus,

f'(x) = 3 + 3x²

Given that f'(x) = 15

substituting the value  f'(x) = 15 in f'(x) = 3 + 3x²

f'(x) = 3 + 3x²

15 =  3 + 3x²

switch sides

3 + 3x² = 15

3x² = 15-3

3x² = 12

Divide both sides by 3

x² = 4

\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}

x=\sqrt{4},\:x=-\sqrt{4}

x=2,\:x=-2

Thus, the value of x​ will be:

x=2,\:x=-2

5 0
2 years ago
Y is directly proportional to x, and y=56 when x=7. find the value of y when x=4.
podryga [215]
Y=kx
when y=56, x=7
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when x=4
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value of y=32
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3 years ago
Correct answer gets 25 points! Help please!
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Y = mx + c

If y = 4, and x = 0, then:

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y = 2

If you plug in the different values of x in each equation, the answer should be:

2,0,-2

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3 years ago
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