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3 years ago

Given that f(x) = x2 + x and g(x) = 3x + 1, find the value of g(f(-2)).

Mathematics

1 answer:

Evgen [1.6K]3 years ago

5 0

Answer:

Step-by-step explanation:

$f(x) = x^2 + x\\g(x) = 3x + 1\\\\g(f(-2)) = ?\\f(-2) =?\\$

To find f(-2) , Substitute -2 for x in the given equation ;

$f(-2)= (-2)^2 +(-2)\\f(-2) = 4-2\\f(-2) = 2$

To find g(f(-2)) ;

$g(f(-2))\\f(-2) =2\\\\= g(f(-2)) = g(2)\\$

To find g(2) , substitute 2 for x in the given equation

$g(x) = 3x+1\\g(2) = 3(2)+1\\\\g(f(-2)) = 6+1\\\\g(f(-2))=7$

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2 years ago

What are the approximate values of the minimum and maximum points of f(x) = x5 − 10x3 + 9x on [-3,3]?

nika2105 [10]

Answer:

Minimum : -37 at x=2.4 and

Maximum = 37 at x=-2.4.

Step-by-step explanation:

Given:

$f(x)=x^5-10x^3+9x$ ; [-3,3]

Explanation:

In order to find minimum/maximum of a function, we need to find the first derivative of the function and then set it equal to 0 to get critical points.

Therefore,

$f'(x)=5x^4-30x^2+9$

Setting derivative equal to 0, we get

$5x^4-30x^2+9=0$

On applying quadratic formula, we get

x=2.4, -2.4, -0.7, 0.7.

So, those are critical points of the given function.

Plugging the values x=2.4, -2.4, -0.7, 0.7, -3 and 3 in above function, we get

f(2.4)=(2.4)^5-10(2.4)^3+9(2.4)= -37.01376 : Minimum.

f(-2.4)=(-2.4)^5-10(-2.4)^3+9(-2.4)= 37.01376 : Maximum.

f(0.7)=(0.7)^5-10(0.7)^3+9(0.7) = 3.03807

f(-0.7)=(-0.7)^5-10(-0.7)^3+9(-0.7) = -3.03807

f(-3)=(-3)^5-10(-3)^3+9(-3) =0

f(3)=(3)^5-10(3)^3+9(3) =0

Therefore the approximate values of the minimum and maximum points of f(x) = $x^5- 10x^3+ 9x$ on [-3,3] are:

Minimum : -37 at x=2.4 and

Maximum = 37 at x=-2.4.

7 0

3 years ago

Given that f(x) = x2 + x and g(x) = 3x + 1, find the value of g(f(-2)).​

Given that f(x) = x2 + x and g(x) = 3x + 1, find the value of g(f(-2)).