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Zepler [3.9K]
3 years ago
10

Let g(x) = 2x and h(x) = x2 + 4. Evaluate (h ∘ g)(1).

Mathematics
1 answer:
anastassius [24]3 years ago
5 0

Answer:

\large\boxed{(h\circ g)(1)=8}

Step-by-step explanation:

(f\circ g)(x)=f\bigg(g(x)\bigg)\\===================\\\\(h\circ g)(1)=h\bigg(g(1)\bigg)\\\\g(1)-\text{put}\ x=1\ \text{to the equation of the function}\ g(x)=2x:\\\\g(1)=2(1)=2\\\\h\bigg(g(1)\bigg)=h(2)-\text{put}\ x=2\ \text{to the equation of the function}\ h(x)=x^2+4:\\\\h(2)=2^2+4=4+4=8

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Answer:

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A stick is 9 m long. A rope is 2 times as long as the stick. If the rope is divided into 3 pieces, how many meters long is each
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3 years ago
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borishaifa [10]

Answer:

f^{-1}(x) = (x + 8)^2

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Step-by-step explanation:

Given

f(x) = \sqrt x - 8

Solving (a): f^{-1}(x)

We have:

f(x) = \sqrt x - 8

Express f(x) as y

y = \sqrt x - 8

Swap x and y

x = \sqrt y - 8

Add 8 to both\ sides

x + 8 = \sqrt y - 8 + 8

x + 8 = \sqrt y

Square both sides

(x + 8)^2 = y

Rewrite as:

y = (x + 8)^2

Express y as: f^{-1}(x)

f^{-1}(x) = (x + 8)^2

To determine the domain, we have:

The original function is f(x) = \sqrt x - 8

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<em>Hence, the domain is:</em>

x \ge -8

3 0
3 years ago
Find the length of the rectangle with a perimeter of 200 cm and breadth of 10 cm.
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Step-by-step explanation:

Given,

Perimeter of the rectangle = 200cm

Breadth of the rectangle = 10 cm

Therefore, by the problem

=> 2(l+b) = 200cm

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4 0
2 years ago
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